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"https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F10352246%2FDodgson_Condensation_The_Historical_and_Mathematical_Development_of_An_Experimental_Method%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F10352246%2FDodgson_Condensation_The_Historical_and_Mathematical_Development_of_An_Experimental_Method%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":36417479,"identifier":"Attachment_36417479","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":10352246,"created_at":"2015-01-27T09:25:58.217-08:00","from_world_paper_id":null,"updated_at":"2024-11-15T19:31:36.892-08:00","_data":{"grobid_abstract":"Dodgson's condensation method has become a powerful tool in the automation of determinant evaluations. In this expository paper I describe its 19th century roots and the major steps on the path that began in the 20th century when the iteration of an identity derived by Dodgson first was studied, including its role in the discovery of the alternating sign matrix conjecture, the evaluation of an important 19th century determinant in partition theory as well as a combinatorial proof of it. I then discuss additional developments that have led the way to its use in modern experimental mathematics.","grobid_abstract_attachment_id":"36417479"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Dodgson Condensation: The Historical and Mathematical Development of An Experimental Method","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [24588114]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div 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data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="10352212" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/10352212/Chios_and_Dodgsons_Determinantal_Identities">Chio's and Dodgson's Determinantal Identities</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="24588114" href="https://kean.academia.edu/FrancineAbeles">Francine F Abeles</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Chio's and Dodgson's Determinantal Identities","attachmentId":36417436,"attachmentType":"pdf","work_url":"https://www.academia.edu/10352212/Chios_and_Dodgsons_Determinantal_Identities","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/10352212/Chios_and_Dodgsons_Determinantal_Identities"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="105019168" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/105019168/Computation_of_Matrix_Determinants_by_Cross_Multiplication_A_Rethinking_of_Dodgson_s_Condensation_and_Reduction_by_Elementary_Row_Operations_Methods">Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="166772615" href="https://independent.academia.edu/JudelProtacio">Judel Protacio</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We formulate a more straightforward, symmetry-based techniques in manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method and strategically applying elementary row operations and the definition and properties of determinants. 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href="https://www.academia.edu/6401898/MORE_CALCULATIONS_ON_DETERMINANT_EVALUATIONS"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="74354647" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74354647/Determinants_Comprehensive_Theory_dd012365751d769cf7df631e54f2d">Determinants Comprehensive Theory dd012365751d769cf7df631e54f2d</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="186363776" href="https://independent.academia.edu/AndreouN">Niki Andreou</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Determinants Comprehensive Theory dd012365751d769cf7df631e54f2d","attachmentId":82537496,"attachmentType":"pdf","work_url":"https://www.academia.edu/74354647/Determinants_Comprehensive_Theory_dd012365751d769cf7df631e54f2d","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74354647/Determinants_Comprehensive_Theory_dd012365751d769cf7df631e54f2d"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="29959309" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/29959309/Play_time_with_determinants">Play time with determinants</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="56899103" href="https://independent.academia.edu/TewodrosAmdeberhan">Tewodros Amdeberhan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2010</p><p class="ds-related-work--abstract ds2-5-body-sm">In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope the reader will find of particular interest.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Play time with determinants","attachmentId":50416520,"attachmentType":"pdf","work_url":"https://www.academia.edu/29959309/Play_time_with_determinants","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/29959309/Play_time_with_determinants"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="678379" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/678379/Schwingers_method_and_the_computation_of_determinants">Schwinger's method and the computation of determinants</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="497230" href="https://independent.academia.edu/LuizAlbuquerque">Luiz Albuquerque</a></div><p class="ds-related-work--metadata ds2-5-body-xs">American …, 1998</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Schwinger's method and the computation of determinants","attachmentId":51296223,"attachmentType":"pdf","work_url":"https://www.academia.edu/678379/Schwingers_method_and_the_computation_of_determinants","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/678379/Schwingers_method_and_the_computation_of_determinants"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":36417479,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":36417479,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_36417479" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="12" data-entity-id="48344821" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/48344821/Qefsere_Gjonbalaj_Armend_Salihu_Computing_the_determinants_of_n_x_n_n_5_matrices_by_reducing_the_order_of_the_determinant_by_four_">Qefsere Gjonbalaj, Armend Salihu “Computing the determinants of n x n (n ≥ 5) matrices by reducing the order of the determinant by four”</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50661863" href="https://independent.academia.edu/qefseregjonbalaj">qefsere gjonbalaj</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Mathematics E - Notes</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link 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href="https://www.academia.edu/83326255/Note_on_the_History_of_Square_Matrix_and_Determinant">Note on the History of (Square) Matrix and Determinant</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26713280" href="https://independent.academia.edu/NiriChoji">Niri Choji</a></div><p class="ds-related-work--metadata ds2-5-body-xs">FUDMA JOURNAL OF SCIENCES</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Note on the History of (Square) Matrix and Determinant","attachmentId":88708436,"attachmentType":"pdf","work_url":"https://www.academia.edu/83326255/Note_on_the_History_of_Square_Matrix_and_Determinant","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span 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