Asymptotic enumeration of symmetric integer matrices with uniform row sums (2013)
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Type of Content
Journal ArticlePublisher
CAMBRIDGE UNIV PRESSISSN
1446788714468107
Language
EnglishCollections
 Science: Journal Articles [1179]
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 zerodiagonal symmetric contingency tables with uniform margins, or loopfree 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.
Citation
McKay BD, McLeod JC (2013). Asymptotic enumeration of symmetric integer matrices with uniform row sums. Journal of the Australian Mathematical Society. 92(3). 367384.This citation is automatically generated and may be unreliable. Use as a guide only.
Keywords
symmetric matrix; asymptotic enumeration; contingency table; multigraph; degree sequenceANZSRC Fields of Research
49  Mathematical sciences::4904  Pure mathematics::490409  Ordinary differential equations, difference equations and dynamical systemsRelated items
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