Partial-twuality polynomials of delta-matroids
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913262717632512 |
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| 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 |
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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 |