Asymptotic enumeration of symmetric integer matrices with uniform row sums

Details Asymptotic enumeration of symmetric integer matrices with uniform row sums Asymptotic enumeration of symmetric integer matrices with uniform row sums

2011-08-23

arxiv.org/abs/1108.4496v1

Mathematics

Combinatorics

Scientific paper

We investigate the number of symmetric matrices of non-negative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero diagonal symmetric contingency tables with uniform margins, or loop-free regular multigraphs. We determine the asymptotic value of this number as the size of the matrix tends to infinity, provided the row sum is large enough. We conjecture that our answer is valid for all row sums.

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