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Bivariate asymptotics via random walks: application to large genus maps
Andrew Elvey Price, Wenjie Fang, Baptiste Louf +1
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two r…
Modularity and Graph Expansion
Baptiste Louf, Colin McDiarmid, Fiona Skerman
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. M…
Large expanders in high genus unicellular maps
Baptiste Louf
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, seve…
Simple formulas for constellations and bipartite maps with prescribed degrees
Baptiste Louf
We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, -angulations), and constellations. These formulas are…
A new family of bijections for planar maps
Baptiste Louf
We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-sl…