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    Asymptotic enumeration of symmetric integer matrices with uniform row sums (2013)

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    Type of Content
    Journal Article
    UC Permalink
    http://hdl.handle.net/10092/15253
    
    Publisher's DOI/URI
    https://doi.org/10.1017/S1446788712000286
    
    Publisher
    CAMBRIDGE UNIV PRESS
    ISSN
    1446-7887
    1446-8107
    Language
    English
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    • Science: Journal Articles [1179]
    Authors
    McKay BD
    McLeod JC
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    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.

    Citation
    McKay BD, McLeod JC (2013). Asymptotic enumeration of symmetric integer matrices with uniform row sums. Journal of the Australian Mathematical Society. 92(3). 367-384.
    This citation is automatically generated and may be unreliable. Use as a guide only.
    Keywords
    symmetric matrix; asymptotic enumeration; contingency table; multigraph; degree sequence
    ANZSRC Fields of Research
    49 - Mathematical sciences::4904 - Pure mathematics::490409 - Ordinary differential equations, difference equations and dynamical systems

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