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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.05601 |
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| _version_ | 1866913097355100160 |
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| author | Zhao, Zhao Yan, Qi |
| author_facet | Zhao, Zhao Yan, Qi |
| contents | Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph and asked under what conditions such a polynomial is even-interpolating, odd-interpolating, or both. In this paper, we provide an answer to this open problem.Using the framework of delta-matroids, we prove that the twist polynomial of any binary delta-matroid is either an even polynomial, an odd polynomial, or both even-interpolating and odd-interpolating. Applying this to ribbon graphs, we deduce that the partial-dual polynomial of any ribbon graph satisfies the same conclusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Twist polynomial interpolation for binary delta-matroids Zhao, Zhao Yan, Qi Combinatorics Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph and asked under what conditions such a polynomial is even-interpolating, odd-interpolating, or both. In this paper, we provide an answer to this open problem.Using the framework of delta-matroids, we prove that the twist polynomial of any binary delta-matroid is either an even polynomial, an odd polynomial, or both even-interpolating and odd-interpolating. Applying this to ribbon graphs, we deduce that the partial-dual polynomial of any ribbon graph satisfies the same conclusion. |
| title | Twist polynomial interpolation for binary delta-matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.05601 |