On the number of Latin squares

BD McKay, Ian Murray Wanless

    Research output: Contribution to journalComment/debate


    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.
    Original languageEnglish
    Pages (from-to)335-344
    Number of pages4
    JournalAnnals of Combinatorics
    Issue number3
    Publication statusPublished - 2005


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