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On large genus asymptotics of certain Hurwitz numbers

Xiang Li

Abstract

In this paper, based on the value of central character on the transposition, we find structure and large genus asymptotics of certain Hurwitz numbers.

On large genus asymptotics of certain Hurwitz numbers

Abstract

In this paper, based on the value of central character on the transposition, we find structure and large genus asymptotics of certain Hurwitz numbers.
Paper Structure (2 sections, 3 theorems, 16 equations)

This paper contains 2 sections, 3 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. The proof of Theorem \ref{['cH2']}

Key Result

Theorem 1.1

For any fixed $d\geq5,s\geq0$ and $\mu^{(1)},\dots,\mu^{(s)}\vdash d$, we have where $b(\mu^{(1)},\dots,\mu^{(s)},m)$ are rational numbers satisfying 1. $b(\mu^{(1)},\dots,\mu^{(s)},\tbinom{d}{2})=1$; 2. $b(\mu^{(1)},\dots,\mu^{(s)},m)=0$, for $\tbinom{d-1}{2}<m<\tbinom{d}{2}$; 3. $b(\mu^{(1)},\dots,\mu^{(s)},\tbinom{d-1}{2})=-d^{2-s}\prod_{i=1}^{s}m_1(\mu^{(i)})$; 4. $b(\mu^{

Theorems & Definitions (5)

  • Theorem 1.1
  • Corollary 1.2
  • proof : Proof of Theorem \ref{['cH2']}
  • Lemma 2.1
  • proof