Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and double simple Hurwitz numbers
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| Publication date | 01-10-2018 |
| Journal | Advances in Mathematics |
| Volume | Issue number | 336 |
| Pages (from-to) | 38-69 |
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| 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. |
| Document type | Article |
| Language | English |
| Published at |
https://doi.org/10.1016/j.aim.2018.07.028
(Final published version)
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