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Simple formulas for constellations and bipartite maps with prescribed degrees
| Content Provider | Semantic Scholar |
|---|---|
| Author | Louf, Baptiste |
| Copyright Year | 2019 |
| Abstract | We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, $2k$-angulations), and constellations. These formulas are the fastest known way of computing these numbers. Our work is a natural extension of previous works on integrable hierarchies (2-Toda and KP), namely the Pandharipande recursion for Hurwitz numbers (proven by Okounkov and simplified by Dubrovin--Yang--Zagier), as well as formulas for several models of maps (Goulden--Jackson, Carrell--Chapuy, Kazarian--Zograf). As for those formulas, a bijective interpretation is still to be found. We also include a formula for monotone simple Hurwitz numbers derived in the same fashion. These formulas also play a key role in subsequent work of the author with T. Budzinski establishing the hyperbolic local limit of random bipartite maps of large genus. |
| File Format | PDF HTM / HTML |
| DOI | 10.4153/s0008414x19000555 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1904.05371v2.pdf |
| Alternate Webpage(s) | http://fpsac2019.fmf.uni-lj.si/resources/Proceedings/91.pdf |
| Alternate Webpage(s) | https://doi.org/10.4153/s0008414x19000555 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
