A recursion for the twist polynomial of a one-point join of normal binary delta-matroids
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918198979330048 |
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| author | Li, Charlton |
| author_facet | Li, Charlton |
| contents | The partial-dual Euler-genus polynomial was defined by Gross, Mansour, and Tucker to analyze how the Euler genus of a ribbon graph changes under partial duality, a generalization of Euler-Poincaré duality introduced by Chmutov. The twist polynomial defined by Yan and Jin extends the partial-dual Euler-genus polynomial to a polynomial on delta-matroids. We derive a recursion formula for the twist polynomial of a one-point join of looped simple graphs -- equivalently, normal, binary delta-matroids. Our recursion applies to the partial-dual Euler-genus polynomial as a special case, where it generalizes a recursion obtained by Yan and Jin. We obtain relations for the twist polynomial on looped simple graphs evaluated at $-1/2$ and for the twist polynomial of a graph with a single looped vertex. A characterization is given for the feasible sets of the delta-matroid associated to a one-point join of looped simple graphs. We show that Yan and Jin's recursion extends to the twist polynomial on delta-matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A recursion for the twist polynomial of a one-point join of normal binary delta-matroids Li, Charlton Combinatorics 05B35, 05C31, 05C10 The partial-dual Euler-genus polynomial was defined by Gross, Mansour, and Tucker to analyze how the Euler genus of a ribbon graph changes under partial duality, a generalization of Euler-Poincaré duality introduced by Chmutov. The twist polynomial defined by Yan and Jin extends the partial-dual Euler-genus polynomial to a polynomial on delta-matroids. We derive a recursion formula for the twist polynomial of a one-point join of looped simple graphs -- equivalently, normal, binary delta-matroids. Our recursion applies to the partial-dual Euler-genus polynomial as a special case, where it generalizes a recursion obtained by Yan and Jin. We obtain relations for the twist polynomial on looped simple graphs evaluated at $-1/2$ and for the twist polynomial of a graph with a single looped vertex. A characterization is given for the feasible sets of the delta-matroid associated to a one-point join of looped simple graphs. We show that Yan and Jin's recursion extends to the twist polynomial on delta-matroids. |
| title | A recursion for the twist polynomial of a one-point join of normal binary delta-matroids |
| topic | Combinatorics 05B35, 05C31, 05C10 |
| url | https://arxiv.org/abs/2511.09504 |