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arXiv · 1409.0632

Partial duality of hypermaps

Sergei Chmutov·Fabien Vignes-Tourneret
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Abstract

We introduce partial duality of hypermaps, which include the classical Euler-Poincaré duality as a particular case. Combinatorially, hypermaps may be described in one of three ways: as three involutions on the set of flags (bi-rotation system or $τ$-model), or as three permutations on the set of half-edges (rotation system or $σ$-model in orientable case), or as edge 3-coloured graphs. We express partial duality in each of these models. We give a formula for the genus change under partial duality.

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Sergei Chmutov, Fabien Vignes-Tourneret. 2021-02-09. Partial duality of hypermaps. https://arxiv.org/abs/1409.0632

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