Asymptotic enumeration of contingency tables
Seminar Room 1, Newton Institute
Contingency tables are nonnegative integer matrices with given row and column sums. Such matrices appear in many combinatorial contexts and have applications in statistics. There has been a lot of work on efficient algorithms for approximately counting these matrices using Markov chains or dynamic programming.
Asymptotic formulae for these matrices have recently been obtained for sufficiently sparse matrices (Greenhill & McKay) and for sufficiently dense matrices when all row sums are equal and all column sums are equal (Canfield & McKay). I will discuss these results and ask whether they provide a practical method for approximate counting.
Joint work with Brendan McKay.
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