Hultman numbers, polygon gluings and matrix integrals

TL;DR

This paper introduces new interpretations of Hultman numbers through polygon gluings and matrix integrals, providing insights into their properties and connections to genome rearrangements.

Contribution

It offers two novel interpretations of Hultman numbers and explores their generating functions, linking combinatorics, topology, and matrix analysis.

Findings

Hultman numbers relate to polygon gluings and matrix integrals.

Derived properties of their generating functions.

Established connections to genome rearrangement models.

Abstract

The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the Hultman numbers: in terms of polygon gluings and as integrals over the space of complex matrices, and derive some properties of their generating functions.