{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:46:10Z","timestamp":1706057170446},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2010,11,1]],"date-time":"2010-11-01T00:00:00Z","timestamp":1288569600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2010,11]]},"DOI":"10.1007\/s00493-010-2426-1","type":"journal-article","created":{"date-parts":[[2011,3,18]],"date-time":"2011-03-18T20:19:26Z","timestamp":1300479566000},"page":"655-680","source":"Crossref","is-referenced-by-count":14,"title":["Asymptotic enumeration of integer matrices with large equal row and column sums"],"prefix":"10.1007","volume":"30","author":[{"given":"E.","family":"Rodney Canfield","sequence":"first","affiliation":[]},{"given":"Brendan D.","family":"McKay","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,3,19]]},"reference":[{"key":"2426_CR1","unstructured":"M. Beck and S. Robins: Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra, Springer, 2007."},{"key":"2426_CR2","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/s00454-003-2850-8","volume":"30","author":"M. Beck","year":"2003","unstructured":"M. Beck and D. Pixton: The Ehrhart polynomial of the Birkhoff polytope, Discrete Comput. Geom. 30 (2003), 623\u2013637.","journal-title":"Discrete Comput. Geom."},{"key":"2426_CR3","first-page":"343","volume":"7","author":"A. B\u00e9k\u00e9ssy","year":"1972","unstructured":"A. B\u00e9k\u00e9ssy, P. B\u00e9k\u00e9ssy and J. Koml\u00f3s: Asymptotic enumeration of regular matrices, Studia Sci. Math. Hungar. 7 (1972), 343\u2013353.","journal-title":"Studia Sci. Math. Hungar."},{"key":"2426_CR4","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0012-365X(74)90118-6","volume":"10","author":"E. A. Bender","year":"1974","unstructured":"E. A. Bender: The asymptotic number of nonnegative integer matrices with given row and column sums, Discrete Math. 10 (1974), 345\u2013353.","journal-title":"Discrete Math."},{"key":"2426_CR5","unstructured":"A. Barvinok and J. A. Hartigan: An asymptotic formula for the number ofnon-negative integer matrices with prescribed row and column sums, arXiv:0910.2477v2."},{"key":"2426_CR6","unstructured":"A. Barvinok, A. Samorodnitsky and A. Yong: Counting magic squares in quasipolynomial time, arXiv:math\/0703227v1."},{"key":"2426_CR7","doi-asserted-by":"crossref","unstructured":"R. Brualdi: Combinatorial Matrix Classes, Cambridge University Press, 2006.","DOI":"10.1017\/CBO9780511721182"},{"key":"2426_CR8","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.jcta.2007.03.009","volume":"115","author":"E. R. Canfield","year":"2008","unstructured":"E. R. Canfield, C. Greenhill and B. D. McKay: Asymptotic enumeration of dense 0\u20131 matrices with specified line sums, J. Combin. Theory Ser. A 115 (2008), 32\u201366.","journal-title":"J. Combin. Theory Ser. A"},{"key":"2426_CR9","doi-asserted-by":"crossref","first-page":"R29","DOI":"10.37236\/1926","volume":"12","author":"E. R. Canfield","year":"2005","unstructured":"E. R. Canfield and B. D. McKay: Asymptotic enumeration of dense 0\u20131 matrices with equal row sums and equal column sums, Electron. J. Combin. 12 (2005), R29.","journal-title":"Electron. J. Combin."},{"key":"2426_CR10","unstructured":"E. R. Canfield and B. D. McKay: The asymptotic volume of the Birkhoff polytope, Online J. Anal. Comb. 4 (2009), Article No. 2."},{"key":"2426_CR11","unstructured":"E. R. Canfield and B. D. McKay: Asymptotic enumeration of highly oblong integer matrices with given row and column sums, in preparation."},{"key":"2426_CR12","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1198\/016214504000001303","volume":"100","author":"Y. Chen","year":"2005","unstructured":"Y. Chen, P. Diaconis, S. P. Holmes and J. S. Liu: Sequential Monte Carlo methods for statistical analysis of tables, J. Amer. Statist. Assoc. 100 (2005), 109\u2013120.","journal-title":"J. Amer. Statist. Assoc."},{"key":"2426_CR13","first-page":"875","volume":"7","author":"S. X. Chen","year":"1997","unstructured":"S. X. Chen and J. S. Liu: Statistical Applications of the Poisson-Binomial and conditional Bernoulli distributions, Statist. Sinica 7 (1997), 875\u2013892.","journal-title":"Statist. Sinica"},{"key":"2426_CR14","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1214\/aos\/1176349634","volume":"13","author":"P. Diaconis","year":"1985","unstructured":"P. Diaconis and B. Efron: Testing for independence in a two-way table: new interpretations of the chi-square statistic (with discussion), Ann. Statist. 13 (1985), 845\u2013913.","journal-title":"Ann. Statist."},{"key":"2426_CR15","doi-asserted-by":"crossref","unstructured":"P. Diaconis and A. Gangolli: Rectangular arrays with fixed margins, in: IMA Volumes on Mathematics and its Applications, volume 72, pages 15\u201341. (Proceedings of the conference on Discrete Probability and Algorithms, Minneapolis, MN, 1993.)","DOI":"10.1007\/978-1-4612-0801-3_3"},{"key":"2426_CR16","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1002\/(SICI)1098-2418(199707)10:4<487::AID-RSA4>3.0.CO;2-Q","volume":"10","author":"M. Dyer","year":"1997","unstructured":"M. Dyer, R. Kannan and J. Mount: Sampling contingency tables, Random Structures Algorithms, 10 (1997), 487\u2013506.","journal-title":"Random Structures Algorithms"},{"key":"2426_CR17","first-page":"33","volume":"1","author":"C. J. Everett Jr.","year":"1971","unstructured":"C. J. Everett, Jr. and P. R. Stein: The asymptotic number of integer stochastic matrices, Discrete Math. 1 (1971), 33\u201372.","journal-title":"Discrete Math."},{"key":"2426_CR18","doi-asserted-by":"crossref","first-page":"859","DOI":"10.2307\/2286475","volume":"72","author":"M. Gail","year":"1977","unstructured":"M. Gail and N. Mantel: Counting the number of r \u00d7 c contingency tables with fixed margins, J. Amer. Statist. Assoc. 72 (1977), 859\u2013862.","journal-title":"J. Amer. Statist. Assoc."},{"key":"2426_CR19","volume-title":"Probability and the Weighing of Evidence","author":"I. J. Good","year":"1950","unstructured":"I. J. Good: Probability and the Weighing of Evidence, Charles Griffin, London, 1950."},{"key":"2426_CR20","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1214\/aos\/1176343649","volume":"4","author":"I. J. Good","year":"1976","unstructured":"I. J. Good: On the application of symmetric Dirichlet distributions and their mixtures to contingency tables, Ann. Statist. 4 (1976), 1159\u20131189.","journal-title":"Ann. Statist."},{"key":"2426_CR21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0012-365X(77)90117-0","volume":"19","author":"I. J. Good","year":"1977","unstructured":"I. J. Good and J. F. Crook: The enumeration of arrays and a generalization related to contingency tables, Discrete Math. 19 (1977), 23\u201345.","journal-title":"Discrete Math."},{"key":"2426_CR22","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.aam.2008.01.002","volume":"41","author":"C. S. Greenhill","year":"2008","unstructured":"C. S. Greenhill and B. D. McKay: Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums, Adv. Appl. Math. 41 (2008), 459\u2013481.","journal-title":"Adv. Appl. Math."},{"key":"2426_CR23","first-page":"87","volume":"1","author":"F. Greselin","year":"2003","unstructured":"F. Greselin: Counting and enumerating frequency tables with given margins, Statistica & Applicazioni (Univ. Milano, Bicocca) 1 (2003), 87\u2013104. Preprint available at http:\/\/hdl.handle.net\/10281\/4643 .","journal-title":"Statistica & Applicazioni (Univ. Milano, Bicocca)"},{"key":"2426_CR24","doi-asserted-by":"crossref","first-page":"13","DOI":"10.2307\/2282952","volume":"58","author":"W. Hoeffding","year":"1963","unstructured":"W. Hoeffding: Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963), 13\u201330.","journal-title":"J. Amer. Statist. Assoc."},{"key":"2426_CR25","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1214\/aos\/1033066199","volume":"24","author":"R. B. Holmes","year":"1996","unstructured":"R. B. Holmes and L. K. Jones: On uniform generation of two-way tables with fixed margins and the conditional volume Test of Diaconis and Efron, Ann. Statist. 24 (1996), 64\u201368.","journal-title":"Ann. Statist"},{"key":"2426_CR26","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1098\/rsta.1900.0021","volume":"194","author":"P. A. Macmahon","year":"1900","unstructured":"P. A. Macmahon: Combinatorial analysis. The foundation of a new theory, Philos. Trans. Roy. Soc. London Ser. A 194 (1900), 361\u2013386. (Paper 57 of Volume I of the Collected Papers.)","journal-title":"Philos. Trans. Roy. Soc. London Ser. A"},{"key":"2426_CR27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1112\/plms\/s2-17.1.25","volume":"17","author":"P. A. Macmahon","year":"1918","unstructured":"P. A. Macmahon: Combinations derived from m identical sets of n different letters, Proc. London Math. Soc. (2) 17 (1918), 25\u201341. (Paper 89 of Volume I of the Collected Papers.)","journal-title":"Proc. London Math. Soc. (2)"},{"key":"2426_CR28","first-page":"207","volume":"40","author":"B. D. McKay","year":"1983","unstructured":"B. D. McKay: Applications of a technique for labelled enumeration, Congressus Numerantium 40 (1983), 207\u2013221.","journal-title":"Congressus Numerantium"},{"key":"2426_CR29","unstructured":"B. D. McKay: Asymptotics for 0\u20131 matrices with prescribed line sums, in: Enumeration and Design, pages 225\u2013238, Academic Press, 1984."},{"key":"2426_CR30","unstructured":"B. D. McKay and J. C. McLeod: Asymptotic enumeration of symmetric integer matrices with uniform row sums, submitted."},{"key":"2426_CR31","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0024-3795(03)00506-8","volume":"373","author":"B. D. McKay","year":"2003","unstructured":"B. D. McKay and X. Wang: Asymptotic enumeration of 0\u20131 matrices with equal row sums and equal column sums, Linear Algebra Appl. 373 (2003), 273\u2013288.","journal-title":"Linear Algebra Appl."},{"key":"2426_CR32","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/S0195-6698(13)80042-X","volume":"11","author":"B. D. McKay","year":"1990","unstructured":"B. D. McKay and N. C. Wormald: Asymptotic enumeration by degree sequence of graphs of high degree, European J. Combin. 11 (1990), 565\u2013580.","journal-title":"European J. Combin."},{"key":"2426_CR33","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/rsa.10049","volume":"21","author":"B. Morris","year":"2002","unstructured":"B. Morris: Improved bounds for sampling contingency tables, Random Structures and Algorithms 21 (2002), 135\u2013146.","journal-title":"Random Structures and Algorithms"},{"key":"2426_CR34","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1109\/18.850669","volume":"46","author":"E. Ordentlich","year":"2000","unstructured":"E. Ordentlich and R. M. Roth: Two-dimensional weight-constrained codes through enumeration bounds, IEEE Trans. Inform. Theory 46 (2000), 1292\u20131301.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"2426_CR35","unstructured":"R. C. Read: Some enumeration problems in graph theory (Doctoral Thesis), University of London, (1958)."},{"key":"2426_CR36","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511805967","volume-title":"Enumerative Combinatorics","author":"R. P. Stanley","year":"1997","unstructured":"R. P. Stanley: Enumerative Combinatorics, Vol. 1, corrected reprint of the 1986 original, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997."},{"key":"2426_CR37","doi-asserted-by":"crossref","unstructured":"R. P. Stanley: Combinatorics and Commutative Algebra, volume 41 of the Progress in Mathematics series, Birkh\u00e4user, 1983.","DOI":"10.1007\/978-1-4899-6752-7"},{"key":"2426_CR38","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0167-5060(08)70717-9","volume":"6","author":"R. P. Stanley","year":"1980","unstructured":"R. P. Stanley: Decompositions of rational convex polyhedra, Ann. Discrete Math. 6 (1980), 333\u2013342.","journal-title":"Ann. Discrete Math."},{"key":"2426_CR39","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1215\/S0012-7094-76-04342-8","volume":"43","author":"R. P. Stanley","year":"1976","unstructured":"R. P. Stanley: Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings; Duke Math. J. 43 (1976), 511\u2013531.","journal-title":"Duke Math. J."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-010-2426-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-010-2426-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-010-2426-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,17]],"date-time":"2020-06-17T12:41:22Z","timestamp":1592397682000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-010-2426-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11]]},"references-count":39,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,11]]}},"alternative-id":["2426"],"URL":"https:\/\/doi.org\/10.1007\/s00493-010-2426-1","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11]]}}}