Asymptotic enumeration of symmetric integer matrices with uniform row sums
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.
|Collections||ANU Research Publications|
|Source:||Journal of the Australian Mathematical Society|
|01_McKay_Asymptotic_enumeration_of_2012.pdf||162.83 kB||Adobe PDF||Request a copy|
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.