English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We obtain simple quadratic recurrence formulas counting bipartite maps onsurfaces with prescribed degrees (in particular, $2k$-angulations), andconstellations. These formulas are the fastest known way of computing thesenumbers. Our work is a natural extension of previous works on integrablehierarchies (2-Toda and KP), namely the Pandharipande recursion for Hurwitznumbers (proven by Okounkov and simplified by Dubrovin-Yang-Zagier), as well asformulas for several models of maps (Goulden-Jackson, Carrell-Chapuy,Kazarian-Zograf). As for those formulas, a bijective interpretation is still tobe found. We also include a formula for monotone simple Hurwitz numbers derivedin the same fashion. These formulas also play a key role in subsequent work ofthe author with T. Budzinski establishing the hyperbolic local limit of randombipartite maps of large genus.

Simple formulas for constellations and bipartite maps with prescribed degrees