{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:41:17Z","timestamp":1740123677078,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,1,9]],"date-time":"2021-01-09T00:00:00Z","timestamp":1610150400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,9]],"date-time":"2021-01-09T00:00:00Z","timestamp":1610150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s11075-020-01059-5","type":"journal-article","created":{"date-parts":[[2021,1,9]],"date-time":"2021-01-09T13:05:11Z","timestamp":1610197511000},"page":"837-851","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fast computation of multinomial coefficients"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3884-2177","authenticated-orcid":false,"given":"Leonardo C.","family":"Araujo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jo\u00e3o P. H.","family":"Sans\u00e3o","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adriano S.","family":"Vale-Cardoso","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,9]]},"reference":[{"key":"1059_CR1","unstructured":"IEEE: Standard for floating-point arithmetic (2008)"},{"key":"1059_CR2","unstructured":"Araujo, L.: Bincoeff. https:\/\/github.com\/leolca\/bincoeff (2019)"},{"key":"1059_CR3","doi-asserted-by":"publisher","unstructured":"Araujo, L.C., Sansa\u0307o, JP.H., Vale-Cardoso, A.S.: Fast computation of binomial coefficients. Numerical Algorithms https:\/\/doi.org\/10.1007\/s11075-020-00912-x (2020)","DOI":"10.1007\/s11075-020-00912-x"},{"key":"1059_CR4","doi-asserted-by":"crossref","unstructured":"Comtet, L.: Advanced Combinatorics: The art of finite and infinite expansions. D. Reidel. ISBN 9027703809 (1974)","DOI":"10.1007\/978-94-010-2196-8"},{"key":"1059_CR5","unstructured":"Eaton, J.W.: Gnu octave (version 5.1.0). https:\/\/octave.org\/doc\/v5.1.0\/Numeric-Data-Types.html (2018)"},{"issue":"1","key":"1059_CR6","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1145\/103162.103163","volume":"23","author":"D Goldberg","year":"1991","unstructured":"Goldberg, D.: What every computer scientist should know about floating-point arithmetic. ACM Comput. Surveys (CSUR) 23 (1), 5\u201348 (1991)","journal-title":"ACM Comput. Surveys (CSUR)"},{"key":"1059_CR7","first-page":"351","volume":"9","author":"VE Hoggatt","year":"1971","unstructured":"Hoggatt, V.E., Alexanderson, G.L.: A property of multinomial coefficients. Fibonacci Quarter. 9, 351\u2013356 (1971)","journal-title":"Fibonacci Quarter."},{"issue":"3","key":"1059_CR8","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1016\/j.csda.2006.05.008","volume":"51","author":"F Izsa\u0307k","year":"2006","unstructured":"Izsa\u0307k, F.: Maximum likelihood estimation for constrained parameters of multinomial distributions\u2013application to zipf\u2013mandelbrot models. Comput Stat Data Anal 51(3), 1575\u20131583 (2006). https:\/\/doi.org\/10.1016\/j.csda.2006.05.008","journal-title":"Comput Stat Data Anal"},{"key":"1059_CR9","unstructured":"Kochurkin, I.: How do i compute multinomials efficiently? Mathematics Stack Exchange. https:\/\/math.stackexchange.com\/q\/204150. (version: 2012-09-28) (2012)"},{"key":"1059_CR10","unstructured":"Hornik, K.: Bincoeff function in GNU Octave (1994)"},{"issue":"4","key":"1059_CR11","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1145\/820127.820168","volume":"34","author":"Y Manolopoulos","year":"2002","unstructured":"Manolopoulos, Y.: Binomial coefficient computation. ACM SIGCSE Bull 34(4), 65 (2002). https:\/\/doi.org\/10.1145\/820127.820168","journal-title":"ACM SIGCSE Bull"},{"key":"1059_CR12","unstructured":"McKeeman, B.: Matlab performance measurement. Technical report, Mathworks. https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/18510-matlab-performance-measurement. [Online; Accessed 03 Feb 2020] (2008)"},{"key":"1059_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4705-6","volume-title":"Handbook of Floating-Point Arithmetic","author":"J-M Muller","year":"2010","unstructured":"Muller, J.-M., Brisebarre, N., de Dinechin, F., Jeannerod, C.-P., Lef\u0117vre, V., Melquiond, G., Revol, N., Stehl\u0117, D., Torres, S.: Handbook of Floating-Point Arithmetic. Birkh\u00e4user, Boston (2010)"},{"key":"1059_CR14","volume-title":"Lehrbuch Der Kombinatorik","author":"E Netto","year":"1958","unstructured":"Netto, E.: Lehrbuch Der Kombinatorik. Chelsea, New York (1958)"},{"issue":"3","key":"1059_CR15","doi-asserted-by":"publisher","first-page":"239","DOI":"10.2307\/1559040","volume":"33","author":"TJ Osler","year":"2002","unstructured":"Osler, T.J.: Fermat\u2019s little theorem from the multinomial theorem. College Math. J. 33(3), 239 (2002). https:\/\/doi.org\/10.2307\/1559040","journal-title":"College Math. J."},{"key":"1059_CR16","unstructured":"Pinote, T.S.: Investigations in computer-aided mathematics:experimentation, computation, and certification. PhD dissertation, Universit\u00e9 Paris-Saclay (2018)"},{"issue":"2","key":"1059_CR17","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1145\/571922.571950","volume":"33","author":"T Rolfe","year":"2001","unstructured":"Rolfe, T.: Binomial coefficient recursion. ACM SIGCSE Bull. 33 (2), 35 (2001). https:\/\/doi.org\/10.1145\/571922.571950","journal-title":"ACM SIGCSE Bull."},{"issue":"5","key":"1059_CR18","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1137\/S1064827593247023","volume":"17","author":"JC Schatzman","year":"1996","unstructured":"Schatzman, J.C.: Accuracy of the discrete Fourier transform and the fast Fourier transform. SIAM J. Sci. Comput. 17(5), 1150\u20131166 (1996)","journal-title":"SIAM J. Sci. Comput."},{"key":"1059_CR19","unstructured":"Wells, D.: The penguin dictionary of curious and interesting numbers. Penguin Books. ISBN 0140080295 (1987)"},{"key":"1059_CR20","unstructured":"Wikipedia contributors: Double-precision floating-point format - Wikipedia, the free encyclopedia. https:\/\/en.wikipedia.org\/wiki\/Double-precision_floating-point_format. [Online; Accessed 20 Mar 2020] (2020a)"},{"key":"1059_CR21","unstructured":"Wikipedia contributors: Floating-point arithmetic. https:\/\/en.wikipedia.org\/wiki\/Floating-point_arithmetic. [Online; Accessed 26 Mar 2020] (2020b)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-01059-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-020-01059-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-01059-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T10:32:35Z","timestamp":1631529155000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-020-01059-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,9]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1059"],"URL":"https:\/\/doi.org\/10.1007\/s11075-020-01059-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2021,1,9]]},"assertion":[{"value":"6 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}