Asymptotic enumeration of lonesum matrices
Abstract
We provide bivariate asymptotics for the poly-Bernoulli numbers, a combinatorial array that enumerates lonesum matrices, using the methods of Analytic Combinatorics in Several Variables (ACSV). For the diagonal asymptotic (i.e., for the special case of square lonesum matrices) we present an alternative proof based on Parseval's identity. In addition, we provide an application in Algebraic Statistics on the asymptotic ML-degree of the bivariate multinomial missing data problem, and we strengthen an existing result on asymptotic enumeration of permutations having a specified excedance set.
Keywords
Cite
@article{arxiv.1912.08850,
title = {Asymptotic enumeration of lonesum matrices},
author = {Jessica Khera and Erik Lundberg and Stephen Melczer},
journal= {arXiv preprint arXiv:1912.08850},
year = {2020}
}
Comments
16 pages, 3 figures. This version includes a more detailed discussion of applications with two new sections related to an application in Algebraic Statistics. The paper will appear in the journal Advances in Applied Mathematics