This paper derives an explicit formula for generating series of l-hypermaps, generalizing results for ribbon graphs, indicating its broader applications.
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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Huang et al. (2025) studied this question.
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