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arXiv · 2501.11215

Enumerating Partial Duals of Hypermaps by Genus

Wenwen Liu·Yichao Chen
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Abstract

The concept of partial duality in hypermaps was introduced by Chmutov and Vignes-Tourneret, and Smith independently. This notion serves as a generalization of the concept of partial duality found in maps. In this paper, we first present an Euler-genus formula concerning the partial duality of hypermaps, which serves as an invariant related to the result obtained by Chmutov and Vignes-Tourneret. This formulation also generalizes the result of Gross, Mansour, and Tucker regarding partial duality in maps. Subsequently, we enumerate the distribution of partial dual Euler-genus for hypermaps and compute the corresponding polynomial for specific classes of hypermaps through three operations: join, bar-amalgamation, and subdivision.

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Wenwen Liu, Yichao Chen. 2025-01-20. Enumerating Partial Duals of Hypermaps by Genus. https://arxiv.org/abs/2501.11215

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