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On the number of Latin squares

McKay, BD and Wanless, IM (2005). On the number of Latin squares. Annals of Combinatorics,9(3):335-344.

Document type: Journal Article
Citation counts: TR Web of Science Citation Count  Cited 38 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 44 times in Scopus Article | Citations

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ISI LOC 000241668800008
Title On the number of Latin squares
Author McKay, BD
Wanless, IM
Journal Name Annals of Combinatorics
Publication Date 2005
Volume Number 9
Issue Number 3
ISSN 0218-0006   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-26044433646
Start Page 335
End Page 344
Total Pages 4
Place of Publication Switzerland
Publisher Birkhauser Verlag AG
HERDC Category C1 - Journal Article (DEST)
Abstract We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f! where f is a particular integer close to 1/2n (3) provide a formula for the number of Latin squares in terms of permanents of (+1, −1)-matrices, (4) find the extremal values for the number of 1-factorisations of k-regular bipartite graphs on 2n vertices whenever 1 ≤ k ≤ n ≤ 11, (5) show that the proportion of Latin squares with a non-trivial symmetry group tends quickly to zero as the order increases.
DOI http://dx.doi.org/10.1007/s00026-005-0261-7   (check subscription with CDU E-Gateway service for CDU Staff and Students  check subscription with CDU E-Gateway in new window)
 
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