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arXiv · 2501.04178

On the constant partial-dual polynomials of hypermaps

Yibing Xiang·Qi Yan
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Abstract

In this paper, we introduce the partial-dual polynomial for hypermaps, extending the concept from ribbon graphs. We discuss the basic properties of this polynomial and characterize it for hypermaps with exactly one hypervertex containing a non-zero constant term. Additionally, we show that the partial-dual polynomial of a prime connected hypermap $H$ is constant if and only if $H$ is a plane hypermap with a single hyperedge.

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Yibing Xiang, Qi Yan. 2025-01-07. On the constant partial-dual polynomials of hypermaps. https://arxiv.org/abs/2501.04178

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