An arithmetic property of moments of the \(\beta\)-Hermite ensemble and certain map enumerators
type: Item
instance of: scholarly article
title: An arithmetic property of moments of the \(\beta\)-Hermite ensemble and certain map enumerators
zbMATH Open document ID: 1380.05200
author: Amol Aggarwal
published in: The Electronic Journal of Combinatorics
publication date: 2018-02-22T00:00:00Z
full work available at URL: v25i1p29
review text: Summary: Moments of the \(\beta\)-Hermite ensemble are known to be related to the enumerative theory of topological maps. When \(\beta \in \{ 1, 2 \}\), asymptotic information about these moments has been used to deduce asymptotics on the number of maps of given genus, and arithmetic information about these moments can sometimes be explained by underlying group actions on the set of maps. In this paper we establish a new arithmetic property about the \(2q\)-th moment of the \(\beta\)-Hermite ensemble, for any prime \(q \geq 3\) and real number \(\beta > 0\), that has a combinatorial interpretation in terms of maps but no known combinatorial explanation. In the process, we derive several additional results that might be of independent interest, including a general integrality statement and an efficient algorithm for evaluating expectations of multi-part elementary symmetric polynomials of bounded length.
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 6841873
zbMATH Keywords: topological maps
zbMATH Keywords: \(\beta\)-Hermite ensemble
zbMATH Keywords: elementary symmetric functions
describes a project that uses: MOPS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6841873