asymptotic analysis 1enumerative combinatorics 1Eulerian maps 1map enumeration 1orthogonal polynomials 1Painlevé equations 1
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math.CO2026
Universal Asymptotics and Exact Enumeration of Eulerian Maps
Ahmad Barhoumi, Roozbeh Gharakhloo, Nathan Hayford
The paper derives universal asymptotic formulas for counting labeled Eulerian maps of any genus with arbitrary degree sequences, and provides an exact enumeration for genus‑1 maps,…
math.CO2026
Combinatorics of Even-Valent Graphs on Riemann Surfaces
Roozbeh Gharakhloo, Tomas Lasic Latimer
In this paper, we derive explicit formulae for the number of regular even-valent graphs, with fixed minimal embedding genus, in which both the valence parameter and the number of v…