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Asymptotic enumeration of symmetric integer matrices with uniform row sums

McKay, Brendan; McLeod, Jeanette


Abstract 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.

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Journal of the Australian Mathematical Society
DOI: 10.1017/S1446788712000286


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