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On the constant partial-dual polynomials of hypermaps (2501.04178v1)
Published 7 Jan 2025 in math.CO
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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