On enumeration of l-hypermaps

2025/09/15 by Huang, Zhengfei, Yang, Di
#Combinatorics (math.CO) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.11848

Abstract

The l-hypermaps, l≥2, which generalize (dual of) ribbon graphs (l=2 case), are interesting enumerative objects. In this paper, based on a theorem of Carlet--van de Leur--Posthuma--Shadrin and the matrix-resolvent method, we derive an explicit formula for k-point generating series of enumeration of l-hypermaps, which generalizes the one obtained in [30] for the l=2 case. We also generalize a theorem of Dubrovin [29].

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