Completed Cycles Leaky Hurwitz Numbers
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.
Authors
- Danilo Lewański (ORCID: https://orcid.org/0000-0002-9706-008X)
- Maksim Karev
- Davide Accadia
Institutions
- University of Trieste (IT)
- Guangdong Technion-Israel Institute of Technology (CN)
- Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (IT)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-11-01
- DOI
- https://doi.org/10.1093/imrn/rnaf327
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Technion-Israel Institute of Technology
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni