On the Number of Latin Squares
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...[Show more]
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|Source:||Annals of Combinatorics|
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