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href="http://dbpedia.org/resource/Permutation">Permutation</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/class/yago/Substitution107443761">Substitution107443761</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. . </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Permutations_RGB.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">في الرياضيات، تبديلة (جمع تبديلات) أو تبديل (بالإنجليزية: Permutation)‏ هي عملية ترتيب عناصر مجموعة في متسلسلة أو بترتيب معين. إذا كانت العناصر مرتبة، فعملية إعادة ترتيب عناصرها تسمى تبديلا.تختلف التبديلات عن التوافيق والتي تعرف بأنها مختارات لعناصر من مجموعة ما بدون اعتبار الترتيب. على سبيل المثال: يوجد تبديلات للمجموعة وهي كالآتي: .هذه هي جميع الترتيبات الممكنة لمجموعة من عناصر. قلب كلمات لها حروف مختلفة أيضا تشكل نوعا من التبديلات. فأي حروف في أي كلمة مرتبة بترتيب معين لكن قلب أو إعادة ترتيب الحروف يعتبر تبديلا.دراسة تبديلات المجموعات المنتهية موضوع مهم في مجال التوافقيات ونظرية الزمر. تُدرس التبديلات في أغلب فروع الرياضيات وفي مجالات عديدة في العلوم. يتم استخدام التبديلات في علوم الحاسب لتحليل ترتيب خوارزمية وميكانيكا الكم وأيضا في الأحياء. عدد التبديلات التي يمكن أن تخضع لها مجموعة عدد عناصرها هو يساوي مضروب ، والذي يكتب بالصيغة . مضروب هو عملية ضرب جميع الأعداد الصحيحة الموجبة الأقل من أو يساوي . في الجبر وبالتحديد في نظرية الزمر، تبديل المجموعة هو تقابل من المجموعة نحو نفسها. والمقصود بالتقابل هو دالة من إلى حيث يوجد صورة واحدة لكل عنصر. وهـذا مرتبط بإعادة ترتيب عناصر حيث يستبدل كل عنصر بالصورة المقابلة له . فعلى سبيل المثال، ممكن كتابة التبديلة المذكورة اعلاه بالدالة المعرفة كالتالي: . تشكل مجموعة جميع التبديلات الممكنة لمجموعة ما زمرة تُدعى زمرة تبديلات.المهم في هذه الزمرة هو أن عملية تحصيل أي تبديلتين ينتج عنها تبديلة جديدة. ممكن أن تُشكل أي تبديلة لمجموعة عناصر بإحدى طريقتين: إما بترتيب مركباته أو باستخدام اسلوب التعويض لأحد الرموز. بالغالب نستخدم المجموعة لكن لايوجد أيضا مانع لإستخدام أي مجموعة. في إطار التركيبات الابتدائية، يُستخدم مصطلحي التبديلات الجزئية وتبديلات لـ (k-permutations) والتي تعني بترتيب عدد من العناصر المختلفة المختارة من مجموعة ما. وعندما تكون (partial permutations ) تساوي عدد عناصر المجموعة فإن هذين التبديلين يعتبر تبديلات للمجموعة ككل. (ar)</li> <li style="display:none;">Permutace n-prvkové množiny je uspořádaná n-tice obsahující každý prvek právě jednou, takže jednoznačně určuje jedno z možných uspořádání těchto prvků. Odtud (řídce užívané) české synonymum pro permutaci pořadí. Ekvivalentní definice je, že se jedná o n-prvkovou variaci z n prvků. V kombinatorice se také uvažují permutace s opakováním, zahrnující i taková uspořádání prvků, ve kterém se některé prvky vyskytují vícekrát. Obecně je permutace (bez opakování) chápána jako bijektivní zobrazení množiny na sebe. (cs)</li> <li style="display:none;">Permutació en matemàtiques, és una noció que té significats lleugerament diferents, tots ells relacionats amb l'acte de permutar (rearranjar) objectes o valors. Les permutacions ocorren, en maneres més o menys prominents, en gairebé cada domini de les matemàtiques. Les permutacions sorgeixen, també, en l'estudi de l'algorisme d'ordenació en informàtica. Donat un conjunt finit, la permutació és cadascuna de les possibles ordenacions de tots els elements d'aquest conjunt. Per exemple en el conjunt , cada ordenació possible dels seus elements, sense repetir-los, és una permutació. Hi a en total 6 permutacions per a aquests elements: "1,2,3", "1,3,2", "2,1,3", "2,3,1", "3,1,2" i "3,2,1". Alternativament es pot considerar objectes diferents, representats per: fins a l'enèsim. De quantes maneres es poden disposar aquests elements disposant-los en una línia recta? Aquestes maneres d'ordenar tals elements es diuen permutacions. La noció de permutació acostuma a aparèixer en dos contexts: * Com noció fonamental de combinatòria, centrant-se en el problema del seu recompte. * En teoria de grups, al definir els grups simètrics. Les permutacions es fan servir en gairebé totes les branques de les matemàtiques i en molts altres camps de la ciència. En informàtica, s'utilitzen per analitzar algorismes d'ordenació; en física quàntica, per descriure estats de partícules; i en biologia, per descriure seqüències d'ARN. El nombre de permutacions de n objectes diferents és n factorial, normalment escrit com n!, que significa el producte de tots els enters positius menors o iguals a n. (ca)</li> <li style="display:none;">Μια μετάθεση ενός συνόλου αντικειμένων είναι μια τοποθέτηση των αντικειμένων αυτών με μια συγκεκριμένη σειρά. Για παράδειγμα, ας πάρουμε το σύνολο {Α,Β,Γ}.Αυτό το σύνολο έχει 6 μεταθέσεις, τις (Α,Β,Γ),(Α,Γ,Β),(Β,Α,Γ),(Β,Γ,Α),(Γ,Α,Β),(Γ,Β,Α). Ο αριθμός (το πλήθος) των μεταθέσεων συνόλου με ν στοιχεία είναι ν!(νι παραγοντικό, δηλαδή ν(ν-1)(ν-2)...·3·2·1 . Ο ακόλουθος πίνακας είναι βοηθητικός στην κατανόηση της αντιστοιχίας του πλήθους των στοιχείων ενός συνόλου με το πλήθος των δυνατών μεταθέσεών τους. Αριθμός στοιχείων συνόλου - Πλήθος μεταθέσεων 1 → 1!=1 2 → 2!=2 3 → 3!=6 4 → 4!=24 5 → 5!=120 6 → 6!=720 7 → 7!=5.040 8 → 8!=40.320 9 → 9!=362.880 10 → 10!=3.628.800 11 → 11!=39.916.800 12 → 12!=479.001.600 Επισημαίνεται ότι οι μεταθέσεις, σε αντίθεση με τις διατάξεις (λήμμα διάταξη), αφορούν όλα τα στοιχεία ενός συνόλου. (el)</li> <li style="display:none;">En la matematiko permutaĵo estas ĉiu el la eblaj diversaj manieroj vicigi la elementojn de certa aro. Ekzemple, la diversaj permutaĵoj de la elementoj a, b, c estas: abc, acb, bac, bca, cab, cba. La kvanto de eblaj permutaĵoj de n elementoj estas ĉiam n! (do n faktoriale). (eo)</li> <li style="display:none;">Unter einer Permutation (von lateinisch permutare ‚vertauschen‘) versteht man in der Kombinatorik eine Anordnung von Objekten in einer bestimmten Reihenfolge. Je nachdem, ob manche Objekte mehrfach auftreten dürfen oder nicht, spricht man von einer Permutation mit Wiederholung oder einer Permutation ohne Wiederholung. Die Anzahl der Permutationen ohne Wiederholung ergibt sich als Fakultät, während die Anzahl der Permutationen mit Wiederholung über Multinomialkoeffizienten angegeben wird. In der Gruppentheorie ist eine Permutation ohne Wiederholung eine bijektive Selbstabbildung einer in der Regel endlichen Menge, wobei als Referenzmengen meist die ersten natürlichen Zahlen verwendet werden. Die Menge der Permutationen der ersten natürlichen Zahlen bildet mit der Hintereinanderausführung als Verknüpfung die symmetrische Gruppe vom Grad . Das neutrale Element dieser Gruppe stellt die identische Permutation dar, während das inverse Element die inverse Permutation ist. Die Untergruppen der symmetrischen Gruppe sind die Permutationsgruppen. Wichtige Kenngrößen von Permutationen sind ihr Zykeltyp, ihre Ordnung und ihr Vorzeichen. Mit Hilfe der Fehlstände einer Permutation lässt sich auf der Menge der Permutationen fester Länge eine partielle Ordnung definieren. Über ihre Inversionstafel kann zudem jeder Permutation eine eindeutige Nummer in einem fakultätsbasierten Zahlensystem zugeordnet werden. Wichtige Klassen von Permutationen sind zyklische, fixpunktfreie, selbstinverse und alternierende Permutationen. Permutationen besitzen vielfältige Einsatzbereiche innerhalb und außerhalb der Mathematik, beispielsweise in der linearen Algebra (Leibniz-Formel), der Analysis (Umordnung von Reihen), der Graphentheorie und Spieltheorie, der Kryptographie (Verschlüsselungsverfahren), der Informatik (Sortierverfahren) und der Quantenmechanik (Pauli-Prinzip). (de)</li> <li style="display:none;">Matematikan, multzo baten permutazioa, oro har, taldekideak sekuentzia edo batean antolatzea da, edo, multzoa ordenatuta badago, multzo ordenatu baten edo n-kote elementuen ordena edo posizioa aldatzea. "Permutazio" hitzak multzo ordenatu baten ordena lineala aldatzeko egintzari edo prozesuari ere egiten dio erreferentzia. Permutazioak eta konbinazioak desberdinak dira, ordena kontuan hartu gabe multzo bateko kide batzuen hautespenak baitira. Adibidez, n-kote gisa idatzita, multzo osoaren sei permutazio daude, hau da: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2) eta (3, 2, 1). Hauek dira hiru elementuen multzo honen antolamendu posible guztiak. Letra desberdinak dituzten hitzen anagramak ere permutazioak dira: letrak jadanik ordenatuta daude jatorrizko hitzean, eta anagrama letren berrantolaketa da. Multzo finituen permutazioak aztertzea gai garrantzitsua da konbinatoriaren eta talde-teoriaren arloetan. Permutazioak matematikaren ia adar guztietan eta zientziaren beste alor askotan erabiltzen dira. Informatikan, antolamendu-algoritmoak aztertzeko erabiltzen dira; fisika kuantikoan, partikulen egoerak deskribatzeko; eta biologian, RNAren sekuentziak deskribatzeko. n objektu desberdinen permutazio kopurua n faktoriala da, normalean n! bezala idazten dena, eta n baino txikiagoak edo berdinak diren osoko positibo guztien biderkadura adierazten du. Multzo baten permutazio guztien multzoak izeneko taldea osatzen du. Taldeko eragiketa osaera da (elkarren segidan bi berrantolaketa egitea), eta horren ondorioz beste berrantolamendu bat lortzen da. Permutazioen propietateak multzoko elementuen izaeraren araberakoak ez direnez, multzoaren permutazioak hartzen dira kontuan permutazioak aztertzeko. (eu)</li> <li style="display:none;">En matemáticas, una permutación de un conjunto es, en términos generales, una disposición de sus miembros en una secuencia u orden lineal, o si el conjunto ya está ordenado, una variación del orden o posición de los elementos de un conjunto ordenado o una tupla. La palabra "permutación" también se refiere al acto o proceso de cambiar el orden lineal de un conjunto ordenado. Las permutaciones difieren de las combinaciones, que son selecciones de algunos miembros de un conjunto sin importar el orden. Por ejemplo, escritas como tuplas, hay seis permutaciones del conjunto {1, 2, 3}, a saber (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2) y (3, 2, 1). Estas son todas las ordenaciones posibles de este conjunto de tres elementos. Los anagramas de palabras cuyas letras son diferentes también son permutaciones: las letras ya están ordenadas en la palabra original, y el anagrama es una reordenación de las letras. El estudio de las permutaciones de es un tema importante en los campos de la combinatoria y la teoría de grupos. Las permutaciones se utilizan en casi todas las ramas de las matemáticas y en muchos otros campos de la ciencia. En informática, se utilizan para analizar algoritmos de ordenación; en física cuántica, para describir estados de partículas; y en biología, para describir secuencias de ARN. El número de permutaciones de n objetos distintos es n factorial, normalmente escrito como n!, que significa el producto de todos los enteros positivos menores o iguales a n. Técnicamente, una permutación de un set S se define como una biyección de S a sí mismo. Es decir, es una función de S a S para la cual cada elemento ocurre exactamente una vez como un valor de imagen. Esto está relacionado con el reordenamiento de los elementos de S en el que cada elemento s es reemplazado por el correspondiente f(s). Por ejemplo, la permutación (3, 1, 2) mencionada anteriormente es descrita por la función definida como . El conjunto de todas las permutaciones de un conjunto forman un llamado grupo simétrico del conjunto. La operación de grupo es la (realizar dos reordenamientos dados sucesivamente), que da como resultado otro reordenamiento. Como las propiedades de las permutaciones no dependen de la naturaleza de los elementos del conjunto, suelen ser las permutaciones del conjunto las que se consideran para estudiar las permutaciones. En combinatoria elemental, las k-permutaciones, o , son los arreglos ordenados de k elementos distintos seleccionados de un conjunto. Cuando k es igual al tamaño del conjunto, son las permutaciones del conjunto. (es)</li> <li style="display:none;">Sa mhatamaitic, is éard is iomalartú ann ná eagar de roinnt rudaí in ord áirithe. Go garbh, is éard atá i gceist le iomalartú tacar, socrú dá chomhaltaí i seicheamh nó in ord líneach, nó má tá an tacar ordaithe cheana féin, atheagrú ar a eilimintí. Má scríobhtar na litreacha A, B agus C ina líne, ceann i ndiaidh a chéile, 6 eagar is féidir a bheith orthu: ABC ACB BAC BCA CAB CBA. Iomalartú a thugtar ar gach eagar; mar sin 6 iomalartú dhifriúla is féidir a bheith ann. Tagraíonn an focal " iomalartú" freisin don ghníomh nó don phróiseas chun ord líneach tacar ordaithe a athrú. (ga)</li> <li>In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers less than or equal to n. Technically, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every element occurs exactly once as an image value. This is related to the rearrangement of the elements of S in which each element s is replaced by the corresponding f(s). For example, the permutation (3, 1, 2) mentioned above is described by the function defined as . The collection of all permutations of a set form a group called the symmetric group of the set. The group operation is the composition (performing two given rearrangements in succession), which results in another rearrangement. As properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set that are considered for studying permutations. In elementary combinatorics, the k-permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. When k is equal to the size of the set, these are the permutations of the set. (en)</li> <li style="display:none;">Permutasi (bahasa Belanda: permutatie, bahasa Inggris: permutation) adalah penyusunan kembali suatu kumpulan objek dalam urutan yang berbeda dari urutan yang semula. Sebagai contoh, kata-kata dalam kalimat sebelumnya dapat disusun kembali sebagai "adalah Permutasi suatu urutan yang berbeda urutan yang kumpulan semula objek penyusunan kembali dalam dari." Proses mengembalikan objek-objek tersebut pada urutan yang baku (sesuai ketentuan) disebut sorting. (in)</li> <li style="display:none;">En mathématiques, la notion de permutation exprime l'idée de réarrangement d'objets discernables. Une permutation d'objets distincts rangés dans un certain ordre correspond à un changement de l'ordre de succession de ces objets. La permutation est une des notions fondamentales en combinatoire, c'est-à-dire pour des problèmes de dénombrement et de probabilités discrètes. Elle sert ainsi à définir et à étudier le carré magique, le carré latin, le sudoku, ou le Rubik's Cube. Les permutations servent également à fonder la théorie des groupes, celle des déterminants, à définir la notion générale de symétrie, etc. (fr)</li> <li style="display:none;">数学における置換（ちかん、英: permutation）の概念は、いくつか僅かに異なった意味で用いられるが、いずれも対象や値を「並べ替える」ことに関するものである。有り体に言えば、対象からなる集合の置換というのは、それらの対象に適当な順番を与えて並べることを言う。例えば、集合 {1, 2, 3} の置換は、 (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1) の全部で六種類ある順序組である。単語のアナグラムは、単語を構成する文字列に対する置換として定められる。そういった意味での置換の研究は、一般には組合せ論に属する話題である。相異なる n 個の対象の置換の総数は n×(n − 1)×(n − 2)×...×2×1 通りであり、これは "n!" と書いて n の階乗と呼ばれる。置換の概念は、多かれ少なかれ（あるいは陰に陽に）、数学のほとんどすべての領域に現れる。たとえばある有限集合上に異なる順序付けが考えられる場合に、単にそれらの順番を無視したいとか、無視した時にどれほどの配置が同一視されるかを知る必要があるなどの理由で、置換が行われることも多い。同様の理由で、置換は計算機科学におけるソートアルゴリズムの研究において生じる。代数学、特に群論において、集合 S 上の置換は S から自身への全単射（つまり写像 S → S で S の各元が像としてちょうど一つずつ現れるもの）として定義される。これは各元 s を対応する f(s) と入れ替えるという意味での S の並べ替え (rearrangement) と関連する。このような置換の全体は対称群と呼ばれる群を成す。重要なことは、置換の合成が定義できること、つまり二つの並べ替えを続けて行うと、それは全体として別の並べ替えになっているということである。S 上の置換は、S の元（あるいはそれを特定の記号によって置き換えたもの）を対象として、それらに対象の並べ替えとして作用する。初等組合せ論において、「順列と置換」はともに n 元集合から k 個の元を取り出す方法として可能なものを数え上げる問題に関するもので、取り出す順番を勘案するのが k-順列、順番を無視するのが k-組合せである。k = n の場合には、k-順列は本項に言う意味での置換となるが、それ以外の場合には順列の項へ譲る。 (ja)</li> <li style="display:none;">Una permutazione è un modo di ordinare in successione oggetti distinti, come nell'anagramma di una parola. In termini matematici una permutazione di un insieme si definisce come una funzione biiettiva . (it)</li> <li style="display:none;">( 다른 뜻에 대해서는 순열 (동음이의) 문서를 참고하십시오.) 수학에서 순열(順列, 문화어: 차례무이, 영어: permutation 퍼뮤테이션[*]) 또는 치환(置換)은 순서가 부여된 임의의 집합을 다른 순서로 뒤섞는 연산이다. 즉, 정의역과 공역이 같은 전단사 함수이다. 개의 원소에 대한 순열의 수는 의 계승 과 같다. 주어진 집합의 순열은 함수의 합성에 따라 대칭군이라고 불리는 군을 이룬다. 이와 같이 주어진 집합의 전부 또는 일부 순열들로 구성된 군(즉, 대칭군의 부분군)을 순열군(順列群, 영어: permutation group)이라고 일컫기도 한다. 예를 들어, 모든 짝순열의 집합은 대칭군의 부분군이며, 이를 교대군이라고 한다. 조합론에서는 더 많은 순열의 개념들이 사용된다. 예컨대 개의 원소에서 개의 원소를 골라 배열하는 방법들의 가짓수는 하강 계승 과 같다. (ko)</li> <li style="display:none;">Permutacja (łac. permutatio „zmiana, wymiana”) – wzajemnie jednoznaczne przekształcenie pewnego zbioru na siebie. Najczęściej termin ten oznacza funkcję na zbiorach skończonych. Permutacje zbiorów skończonych mogą być utożsamiane z ustawianiem elementów zbioru w pewnej kolejności. W poniższym artykule zbiór wszystkich permutacji zbioru będzie oznaczany jeżeli to zapisywany on będzie symbolem (zob. pozostałe oznaczenia w artykule o grupach permutacji). (pl)</li> <li style="display:none;">Een permutatie van een eindige verzameling (van bijvoorbeeld voorwerpen of getallen) is een herschikking ervan, dat wil zeggen het uitvoeren van nul of meer verwisselingen. Uitgaande van een bepaalde beginvolgorde kan men een permutatie verkrijgen door te kiezen welke men als eerste neemt, vervolgens welke van de overige men als tweede neemt, enzovoort tot alle gekozen zijn. Als er een standaardvolgorde is zoals bij de verzameling {1, 2, 3, 4} neemt men deze wel impliciet als beginvolgorde, waardoor de permutaties corresponderen met de mogelijke volgordes. Permutaties zijn onder meer belangrijk in kansrekening, statistiek en combinatoriek. Het begrip kan ook worden gedefinieerd voor een oneindige verzameling. (nl)</li> <li style="display:none;">Em matemática, especialmente na álgebra abstrata e áreas relacionadas, uma permutação é uma bijeção, de um conjunto finito X nele mesmo. Em combinatória, o termo permutação tem um significado tradicional, que é usado para incluir listas ordenadas sem repetição, mas não exaustiva (portanto com menos elementos do que o máximo possível). O conceito de permutação expressa a ideia de que objetos distintos podem ser arranjados em inúmeras ordens diferentes. Por exemplo, com os números de um a seis, cada ordem possível produz uma lista dos números, sem repetições. Uma de tais permutações é: (3, 4, 6, 1, 2, 5). Por exemplo, quando se dá dois passos, um após o outro, podemos ter duas permutações: "pé esquerdo-pé direito" ou "pé direito-pé esquerdo", dependendo apenas do pé que dá o primeiro passo. Um exemplo mais complexo seria o do "change ringing", que é a arte de badalar sinos de afinação distinta em uma série de padrões. Há muitas ordens diferentes na qual um conjunto de seis sinos, cujas afinações diferem entre si, ou seja, cada um com um tom diferente, pode soar. Se os sinos forem numerados de um a seis, cada possível ordem terá uma lista com os números referente a ela e não haverá repetição alguma. Há inúmeras formas de se definir formalmente o conceito de permutação. Uma permutação é uma sequência ordenada contendo cada símbolo de um conjunto uma única vez; tanto (1, 2, 2, 3, 4, 5, 6) quanto (1, 2, 4, 5, 6) não são permutações do conjunto dos números de 1 a 6. Pode-se assim apontar a diferença essencial entre uma permutação e um conjunto: em uma permutação, a ordem é relevante, já que os elementos são arranjados em uma ordem específica. (pt)</li> <li style="display:none;">Перестано́вка в комбинаторике — упорядоченный набор без повторений чисел обычно трактуемый как биекция на множестве , которая числу ставит в соответствие -й элемент из набора. Число при этом называется длиной перестановки. В теории групп под перестановкой произвольного множества подразумевается биекция этого множества на себя. Как синоним слову «перестановка» в этом смысле некоторые авторы используют слово подстановка. (Другие авторы подстановкой называют наглядный способ записи перестановки. Более существенное отличие состоит в том, что подстановка — это непосредственно функция, а перестановка — результат применения этой функции к элементам последовательности.) Термин «перестановка» возник потому, что сначала брались объекты, каким-то образом расставленные, а другие способы упорядочения требовали переставить эти объекты.. Перестановкой называются наборы, состоящие из одного и того же числа элементов, отличающихся только порядком следования элементов. (ru)</li> <li style="display:none;">Inom matematiken används termen permutation i flera besläktade betydelser, nämligen som en funktion, en omordning, eller som ett urval. (sv)</li> <li style="display:none;">排列（英語：Permutation）是將相異物件或符號根據確定的順序重排。每個順序都稱作一個排列。例如，從一到六的數字有720種排列，對應於由這些數字組成的所有不重複亦不闕漏的序列，例如"4, 5, 6, 1, 2, 3" 與1, 3, 5, 2, 4, 6。置換（排列）的廣義概念在不同語境下有不同的形式定義： * 在集合論中，一個集合的置換是從該集合映至自身的雙射；在有限集的情況，便與上述定義一致。 * 在組合數學中，置換一詞的傳統意義是一個有序序列，其中元素不重複，但可能有闕漏。例如1,2,4,3可以稱為1,2,3,4,5,6的一個置換，但是其中不含5,6。此時通常會標明為「從n個對象取r個對象的置換」。 (zh)</li> <li style="display:none;">Перестановкою скінченної множини називається впорядкований набір без повторів із її елементів. Перестановка — довільна бієкція . Усього існує (факторіал) різних перестановок, де (потужність множини (кількість елементів у ній)). 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Odtud (řídce užívané) české synonymum pro permutaci pořadí. Ekvivalentní definice je, že se jedná o n-prvkovou variaci z n prvků. V kombinatorice se také uvažují permutace s opakováním, zahrnující i taková uspořádání prvků, ve kterém se některé prvky vyskytují vícekrát. Obecně je permutace (bez opakování) chápána jako bijektivní zobrazení množiny na sebe. (cs)</li> <li style="display:none;">En la matematiko permutaĵo estas ĉiu el la eblaj diversaj manieroj vicigi la elementojn de certa aro. Ekzemple, la diversaj permutaĵoj de la elementoj a, b, c estas: abc, acb, bac, bca, cab, cba. La kvanto de eblaj permutaĵoj de n elementoj estas ĉiam n! (do n faktoriale). (eo)</li> <li style="display:none;">Sa mhatamaitic, is éard is iomalartú ann ná eagar de roinnt rudaí in ord áirithe. Go garbh, is éard atá i gceist le iomalartú tacar, socrú dá chomhaltaí i seicheamh nó in ord líneach, nó má tá an tacar ordaithe cheana féin, atheagrú ar a eilimintí. Má scríobhtar na litreacha A, B agus C ina líne, ceann i ndiaidh a chéile, 6 eagar is féidir a bheith orthu: ABC ACB BAC BCA CAB CBA. Iomalartú a thugtar ar gach eagar; mar sin 6 iomalartú dhifriúla is féidir a bheith ann. Tagraíonn an focal " iomalartú" freisin don ghníomh nó don phróiseas chun ord líneach tacar ordaithe a athrú. (ga)</li> <li style="display:none;">Permutasi (bahasa Belanda: permutatie, bahasa Inggris: permutation) adalah penyusunan kembali suatu kumpulan objek dalam urutan yang berbeda dari urutan yang semula. Sebagai contoh, kata-kata dalam kalimat sebelumnya dapat disusun kembali sebagai "adalah Permutasi suatu urutan yang berbeda urutan yang kumpulan semula objek penyusunan kembali dalam dari." Proses mengembalikan objek-objek tersebut pada urutan yang baku (sesuai ketentuan) disebut sorting. (in)</li> <li style="display:none;">Una permutazione è un modo di ordinare in successione oggetti distinti, come nell'anagramma di una parola. In termini matematici una permutazione di un insieme si definisce come una funzione biiettiva . (it)</li> <li style="display:none;">( 다른 뜻에 대해서는 순열 (동음이의) 문서를 참고하십시오.) 수학에서 순열(順列, 문화어: 차례무이, 영어: permutation 퍼뮤테이션[*]) 또는 치환(置換)은 순서가 부여된 임의의 집합을 다른 순서로 뒤섞는 연산이다. 즉, 정의역과 공역이 같은 전단사 함수이다. 개의 원소에 대한 순열의 수는 의 계승 과 같다. 주어진 집합의 순열은 함수의 합성에 따라 대칭군이라고 불리는 군을 이룬다. 이와 같이 주어진 집합의 전부 또는 일부 순열들로 구성된 군(즉, 대칭군의 부분군)을 순열군(順列群, 영어: permutation group)이라고 일컫기도 한다. 예를 들어, 모든 짝순열의 집합은 대칭군의 부분군이며, 이를 교대군이라고 한다. 조합론에서는 더 많은 순열의 개념들이 사용된다. 예컨대 개의 원소에서 개의 원소를 골라 배열하는 방법들의 가짓수는 하강 계승 과 같다. (ko)</li> <li style="display:none;">Permutacja (łac. permutatio „zmiana, wymiana”) – wzajemnie jednoznaczne przekształcenie pewnego zbioru na siebie. Najczęściej termin ten oznacza funkcję na zbiorach skończonych. Permutacje zbiorów skończonych mogą być utożsamiane z ustawianiem elementów zbioru w pewnej kolejności. W poniższym artykule zbiór wszystkich permutacji zbioru będzie oznaczany jeżeli to zapisywany on będzie symbolem (zob. pozostałe oznaczenia w artykule o grupach permutacji). (pl)</li> <li style="display:none;">Inom matematiken används termen permutation i flera besläktade betydelser, nämligen som en funktion, en omordning, eller som ett urval. (sv)</li> <li style="display:none;">排列（英語：Permutation）是將相異物件或符號根據確定的順序重排。每個順序都稱作一個排列。例如，從一到六的數字有720種排列，對應於由這些數字組成的所有不重複亦不闕漏的序列，例如"4, 5, 6, 1, 2, 3" 與1, 3, 5, 2, 4, 6。置換（排列）的廣義概念在不同語境下有不同的形式定義： * 在集合論中，一個集合的置換是從該集合映至自身的雙射；在有限集的情況，便與上述定義一致。 * 在組合數學中，置換一詞的傳統意義是一個有序序列，其中元素不重複，但可能有闕漏。例如1,2,4,3可以稱為1,2,3,4,5,6的一個置換，但是其中不含5,6。此時通常會標明為「從n個對象取r個對象的置換」。 (zh)</li> <li style="display:none;">Перестановкою скінченної множини називається впорядкований набір без повторів із її елементів. Перестановка — довільна бієкція . Усього існує (факторіал) різних перестановок, де (потужність множини (кількість елементів у ній)). (uk)</li> <li style="display:none;">في الرياضيات، تبديلة (جمع تبديلات) أو تبديل (بالإنجليزية: Permutation)‏ هي عملية ترتيب عناصر مجموعة في متسلسلة أو بترتيب معين. إذا كانت العناصر مرتبة، فعملية إعادة ترتيب عناصرها تسمى تبديلا.تختلف التبديلات عن التوافيق والتي تعرف بأنها مختارات لعناصر من مجموعة ما بدون اعتبار الترتيب. على سبيل المثال: يوجد تبديلات للمجموعة وهي كالآتي: .هذه هي جميع الترتيبات الممكنة لمجموعة من عناصر. قلب كلمات لها حروف مختلفة أيضا تشكل نوعا من التبديلات. فأي حروف في أي كلمة مرتبة بترتيب معين لكن قلب أو إعادة ترتيب الحروف يعتبر تبديلا.دراسة تبديلات المجموعات المنتهية موضوع مهم في مجال التوافقيات ونظرية الزمر. . (ar)</li> <li style="display:none;">Permutació en matemàtiques, és una noció que té significats lleugerament diferents, tots ells relacionats amb l'acte de permutar (rearranjar) objectes o valors. Les permutacions ocorren, en maneres més o menys prominents, en gairebé cada domini de les matemàtiques. Les permutacions sorgeixen, també, en l'estudi de l'algorisme d'ordenació en informàtica. Donat un conjunt finit, la permutació és cadascuna de les possibles ordenacions de tots els elements d'aquest conjunt. La noció de permutació acostuma a aparèixer en dos contexts: (ca)</li> <li style="display:none;">Μια μετάθεση ενός συνόλου αντικειμένων είναι μια τοποθέτηση των αντικειμένων αυτών με μια συγκεκριμένη σειρά. Για παράδειγμα, ας πάρουμε το σύνολο {Α,Β,Γ}.Αυτό το σύνολο έχει 6 μεταθέσεις, τις (Α,Β,Γ),(Α,Γ,Β),(Β,Α,Γ),(Β,Γ,Α),(Γ,Α,Β),(Γ,Β,Α). Ο αριθμός (το πλήθος) των μεταθέσεων συνόλου με ν στοιχεία είναι ν!(νι παραγοντικό, δηλαδή ν(ν-1)(ν-2)...·3·2·1 . Ο ακόλουθος πίνακας είναι βοηθητικός στην κατανόηση της αντιστοιχίας του πλήθους των στοιχείων ενός συνόλου με το πλήθος των δυνατών μεταθέσεών τους. Αριθμός στοιχείων συνόλου - Πλήθος μεταθέσεων 1 → 1!=1 2 → 2!=2 3 → 3!=6 4 → 4!=24 5 → 5!=120 (el)</li> <li style="display:none;">Unter einer Permutation (von lateinisch permutare ‚vertauschen‘) versteht man in der Kombinatorik eine Anordnung von Objekten in einer bestimmten Reihenfolge. Je nachdem, ob manche Objekte mehrfach auftreten dürfen oder nicht, spricht man von einer Permutation mit Wiederholung oder einer Permutation ohne Wiederholung. Die Anzahl der Permutationen ohne Wiederholung ergibt sich als Fakultät, während die Anzahl der Permutationen mit Wiederholung über Multinomialkoeffizienten angegeben wird. (de)</li> <li style="display:none;">En matemáticas, una permutación de un conjunto es, en términos generales, una disposición de sus miembros en una secuencia u orden lineal, o si el conjunto ya está ordenado, una variación del orden o posición de los elementos de un conjunto ordenado o una tupla. La palabra "permutación" también se refiere al acto o proceso de cambiar el orden lineal de un conjunto ordenado. El número de permutaciones de n objetos distintos es n factorial, normalmente escrito como n!, que significa el producto de todos los enteros positivos menores o iguales a n. . (es)</li> <li style="display:none;">Matematikan, multzo baten permutazioa, oro har, taldekideak sekuentzia edo batean antolatzea da, edo, multzoa ordenatuta badago, multzo ordenatu baten edo n-kote elementuen ordena edo posizioa aldatzea. "Permutazio" hitzak multzo ordenatu baten ordena lineala aldatzeko egintzari edo prozesuari ere egiten dio erreferentzia. Permutazioak matematikaren ia adar guztietan eta zientziaren beste alor askotan erabiltzen dira. Informatikan, antolamendu-algoritmoak aztertzeko erabiltzen dira; fisika kuantikoan, partikulen egoerak deskribatzeko; eta biologian, RNAren sekuentziak deskribatzeko. (eu)</li> <li>In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. . (en)</li> <li style="display:none;">En mathématiques, la notion de permutation exprime l'idée de réarrangement d'objets discernables. Une permutation d'objets distincts rangés dans un certain ordre correspond à un changement de l'ordre de succession de ces objets. (fr)</li> <li style="display:none;">数学における置換（ちかん、英: permutation）の概念は、いくつか僅かに異なった意味で用いられるが、いずれも対象や値を「並べ替える」ことに関するものである。有り体に言えば、対象からなる集合の置換というのは、それらの対象に適当な順番を与えて並べることを言う。例えば、集合 {1, 2, 3} の置換は、 (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1) の全部で六種類ある順序組である。単語のアナグラムは、単語を構成する文字列に対する置換として定められる。そういった意味での置換の研究は、一般には組合せ論に属する話題である。相異なる n 個の対象の置換の総数は n×(n − 1)×(n − 2)×...×2×1 通りであり、これは "n!" と書いて n の階乗と呼ばれる。置換の概念は、多かれ少なかれ（あるいは陰に陽に）、数学のほとんどすべての領域に現れる。たとえばある有限集合上に異なる順序付けが考えられる場合に、単にそれらの順番を無視したいとか、無視した時にどれほどの配置が同一視されるかを知る必要があるなどの理由で、置換が行われることも多い。同様の理由で、置換は計算機科学におけるソートアルゴリズムの研究において生じる。 (ja)</li> <li style="display:none;">Een permutatie van een eindige verzameling (van bijvoorbeeld voorwerpen of getallen) is een herschikking ervan, dat wil zeggen het uitvoeren van nul of meer verwisselingen. Uitgaande van een bepaalde beginvolgorde kan men een permutatie verkrijgen door te kiezen welke men als eerste neemt, vervolgens welke van de overige men als tweede neemt, enzovoort tot alle gekozen zijn. Als er een standaardvolgorde is zoals bij de verzameling {1, 2, 3, 4} neemt men deze wel impliciet als beginvolgorde, waardoor de permutaties corresponderen met de mogelijke volgordes. (nl)</li> <li style="display:none;">Em matemática, especialmente na álgebra abstrata e áreas relacionadas, uma permutação é uma bijeção, de um conjunto finito X nele mesmo. Em combinatória, o termo permutação tem um significado tradicional, que é usado para incluir listas ordenadas sem repetição, mas não exaustiva (portanto com menos elementos do que o máximo possível). O conceito de permutação expressa a ideia de que objetos distintos podem ser arranjados em inúmeras ordens diferentes. (pt)</li> <li style="display:none;">Перестано́вка в комбинаторике — упорядоченный набор без повторений чисел обычно трактуемый как биекция на множестве , которая числу ставит в соответствие -й элемент из набора. Число при этом называется длиной перестановки. Термин «перестановка» возник потому, что сначала брались объекты, каким-то образом расставленные, а другие способы упорядочения требовали переставить эти объекты.. Перестановкой называются наборы, состоящие из одного и того же числа элементов, отличающихся только порядком следования элементов. (ru)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">تبديل (رياضيات) (ar)</li> <li style="display:none;">Permutació (ca)</li> <li style="display:none;">Permutace (cs)</li> <li style="display:none;">Permutation (de)</li> <li style="display:none;">Μετάθεση (μαθηματικά) (el)</li> <li style="display:none;">Permutaĵo (eo)</li> <li style="display:none;">Permutación (es)</li> <li style="display:none;">Permutazio (eu)</li> <li style="display:none;">Iomalartú (ga)</li> <li style="display:none;">Permutasi (in)</li> <li style="display:none;">Permutation (fr)</li> <li style="display:none;">Permutazione (it)</li> <li style="display:none;">置換 (数学) (ja)</li> <li style="display:none;">순열 (ko)</li> <li>Permutation (en)</li> <li style="display:none;">Permutacja (pl)</li> <li style="display:none;">Permutatie (nl)</li> <li style="display:none;">Перестановка (ru)</li> <li style="display:none;">Permutação (pt)</li> <li style="display:none;">Permutation (sv)</li> <li style="display:none;">Перестановка (uk)</li> <li style="display:none;">置換 (zh)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.0c0bw" href="http://rdf.freebase.com/ns/m.0c0bw">freebase:Permutation</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://ru.dbpedia.org/resource/Перестановка" href="http://ru.dbpedia.org/resource/Перестановка">dbpedia-ru:Permutation</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q161519" href="http://www.wikidata.org/entity/Q161519">wikidata:Permutation</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://af.dbpedia.org/resource/Permutasie" 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href="http://dbpedia.org/resource/Alternative_algebra">dbr:Alternative_algebra</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Equivalence_relation" href="http://dbpedia.org/resource/Equivalence_relation">dbr:Equivalence_relation</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Erdős–Ko–Rado_theorem" href="http://dbpedia.org/resource/Erdős–Ko–Rado_theorem">dbr:Erdős–Ko–Rado_theorem</a></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://purl.org/linguistics/gold/hypernym">gold:hypernym</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Unpredictable_permutation" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Unpredictable_permutation">dbr:Unpredictable_permutation</a></li> <li><a class="uri" rev="gold:hypernym" 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prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Separable_permutation">dbr:Separable_permutation</a></li> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Cyclic_permutation" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Cyclic_permutation">dbr:Cyclic_permutation</a></li> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Bit-reversal_permutation" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Bit-reversal_permutation">dbr:Bit-reversal_permutation</a></li> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Symmetry_operation" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Symmetry_operation">dbr:Symmetry_operation</a></li> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Object–verb–subject" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Object–verb–subject">dbr:Object–verb–subject</a></li> <li><a class="uri" rev="gold:hypernym" resource="http://dbpedia.org/resource/Superpattern" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Superpattern">dbr:Superpattern</a></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://xmlns.com/foaf/0.1/primaryTopic">foaf:primaryTopic</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="foaf:primaryTopic" resource="http://en.wikipedia.org/wiki/Permutation" href="http://en.wikipedia.org/wiki/Permutation">wikipedia-en:Permutation</a></li> </ul></td></tr> </tbody> </table> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="text-center p-4 bg-light"> <a href="https://virtuoso.openlinksw.com/" title="OpenLink Virtuoso"><img class="powered_by" src="/statics/images/virt_power_no_border.png" alt="Powered by OpenLink 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