3 citations · 5 across the 4 of their papers we have counts for
4 papers
Map enumeration from a dynamical perspective
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlevé equations) and asymptotic analysis of orthogonal poly…
Non-recursive Counts of Graphs on Surfaces
Nicholas Ercolani, Joceline Lega, Brandon Tippings
The problem of map enumeration concerns counting connected spatial graphs, with a specified number of vertices, that can be embedded in a compact surface of genus in such a…
Multiple Scale Asymptotics of Map Enumeration
Nicholas Ercolani, Joceline Lega, Brandon Tippings
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar…
Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This manuscript develops a novel understanding of non-polar solutions of the discrete Painlevé I equation (dP1). As the non-autonomous counterpart of an analytically completely int…