Skip navigation
Skip navigation

Asymptotic enumeration of symmetric integer matrices with uniform row sums

McKay, Brendan; McLeod, Jeanette

Description

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
URI: http://hdl.handle.net/1885/78395
Source: Journal of the Australian Mathematical Society
DOI: 10.1017/S1446788712000286

Download

File Description SizeFormat Image
01_McKay_Asymptotic_enumeration_of_2012.pdf162.83 kBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  20 July 2017/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator