ASYMPTOTIC ENUMERATION OF SYMMETRIC INTEGER MATRICES WITH UNIFORM ROW SUMS

作者：McKay Brendan D; McLeod Jeanette C^*

来源：Journal of the Australian Mathematical Society, 2012, 92(3): 367-384.

DOI：10.1017/S1446788712000286

• symmetric matrix
• asymptotic enumeration
• contingency table
• multigraph
• degree sequence

We investigate the number of symmetric matrices of nonnegative 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 one form of our answer is valid for all row sums. An example appears in Figure 1.

• 出版日期2012-6