Partial-twuality polynomials of delta-matroids

Fuente: arXiv
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Main Authors: Yan, Qi, Jin, Xian'an
Format: Preprint
Published: 2022
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_version_ 1866913262717632512
author Yan, Qi
Jin, Xian'an
author_facet Yan, Qi
Jin, Xian'an
contents Gross, Mansour and Tucker introduced the partial-twuality polynomial of a ribbon graph. Chumutov and Vignes-Tourneret posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would make sense for general delta-matroids. In this paper we consider analogues of partial-twuality polynomials for delta-matroids. Various possible properties of partial-twuality polynomials of set systems are studied. We discuss the numerical implications of partial-twualities on a single element and prove that the intersection graphs can determine the partial-twuality polynomials of bouquets and normal binary delta-matroids, respectively. Finally, we give a characterization of vf-safe delta-matroids whose partial-twuality polynomials have only one term.
format Preprint
id arxiv_https___arxiv_org_abs_2210_15273
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Partial-twuality polynomials of delta-matroids
Yan, Qi
Jin, Xian'an
Combinatorics
05B35, 05C10, 05C31
Gross, Mansour and Tucker introduced the partial-twuality polynomial of a ribbon graph. Chumutov and Vignes-Tourneret posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would make sense for general delta-matroids. In this paper we consider analogues of partial-twuality polynomials for delta-matroids. Various possible properties of partial-twuality polynomials of set systems are studied. We discuss the numerical implications of partial-twualities on a single element and prove that the intersection graphs can determine the partial-twuality polynomials of bouquets and normal binary delta-matroids, respectively. Finally, we give a characterization of vf-safe delta-matroids whose partial-twuality polynomials have only one term.
title Partial-twuality polynomials of delta-matroids
topic Combinatorics
05B35, 05C10, 05C31
url https://arxiv.org/abs/2210.15273