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arXiv · 2404.13839

On a conjecture of Gross, Mansour and Tucker for $\Delta$-matroids

Remi Cocou Avohou
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Abstract

Gross, Mansour, and Tucker introduced the partial-duality polynomial of a ribbon graph [Distributions, European J. Combin. 86, 1--20, 2020], the generating function enumerating partial duals by the Euler genus. Chmutov and Vignes-Tourneret wondered if this polynomial and its conjectured properties would hold for general delta-matroids, which are combinatorial abstractions of ribbon graphs. Yan and Jin contributed to this inquiry by identifying a subset of delta-matroids-specifically, even normal binary ones-whose twist polynomials are characterized by a singular term. Building upon this foundation, the current paper expands the scope of the investigation to encompass even non-binary delta-matroids, revealing that none of them have width-changing twists.

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Remi Cocou Avohou. 2024-04-22. On a conjecture of Gross, Mansour and Tucker for $\Delta$-matroids. https://arxiv.org/abs/2404.13839

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