Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and simple double Hurwitz numbers

2017/10/03 by Marvin Anas Hahn, Hahn, Marvin Anas, Reinier Kramer +3 · 1 citation
Mathematics · #05A05 #05A15 #14H57 #14N10 #14N35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1710.01047

openalex publication_date 2017/10/03 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals the strong piecewise polynomiality in the sense of Goulden-Jackson-Vakil, generalising a result of Johnson, and provides a new explicit proof of the piecewise polynomiality of the mixed case. Moreover, we derive wall-crossing formulae for the mixed case. These statements specialise to any of the three types of Hurwitz numbers, and to the mixed case of any pair.

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