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arXiv · 2502.00860

Completed Cycles Leaky Hurwitz Numbers

Davide Accadia·Maksim Karev·Danilo Lewański
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Abstract

We introduce $(r+1)$-completed cycles $k$-leaky Hurwitz numbers and prove piecewise polynomiality as well as establishing their chamber polynomiality structure and their wall crossing formulae. For $k=0$ the results recover previous results of Shadrin-Spitz-Zvonkine. The specialization for $r=1$ recovers Hurwitz numbers that are close to the ones studied by Cavalieri-Markwig-Ranganathan and Cavalieri-Markwig-Schmitt. The ramifications differ by a lower order torus correction, natural from the Fock space perspective, not affecting the genus zero enumeration, nor the enumeration for leaky parameter values $k = \pm 1$ in all genera.

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Davide Accadia, Maksim Karev, Danilo Lewański. 2025-02-02. Completed Cycles Leaky Hurwitz Numbers. https://doi.org/10.1093/imrn%2Frnaf327

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