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arXiv · 2604.01190

High genus one part monotone Hurwitz numbers

Simon Barazer·Baptiste Louf
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Abstract

We obtain bivariate asymptotics for one part monotone Hurwitz numbers in high genus (i.e. as both the size and the genus go to infinity). To do so, we start with a linear recurrence for these numbers obtained by Do and Chaudhuri. Then, we apply a recent method developped by Elvey-Price, Fang, Wallner and the second author to extract asymptotics from such recurrences.

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Simon Barazer, Baptiste Louf. 2026-04-01. High genus one part monotone Hurwitz numbers. https://arxiv.org/abs/2604.01190

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