Asymptotic enumeration of symmetric integer matrices with uniform row sums
Combinatorics
2013-01-22 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1108.4496,
title = {Asymptotic enumeration of symmetric integer matrices with uniform row sums},
author = {Brendan D. McKay and Jeanette C. McLeod},
journal= {arXiv preprint arXiv:1108.4496},
year = {2013}
}