Orbits and self-twuality in set systems and delta-matroids
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908598968254464 |
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| author | Li, Zhuo Jin, Xian'an Yan, Qi |
| author_facet | Li, Zhuo Jin, Xian'an Yan, Qi |
| contents | We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This action extends the ribbon group framework of Abrams and Ellis-Monaghan from ribbon graphs to set systems, facilitating a systematic investigation of self-twuality. We prove that different forms of self-twuality propagate through orbits under the group action and establish a characterization of the orbit of a vf-safe delta-matroid via multimatroids. As an application, we analyze orbits of ribbon-graphic delta-matroids. Our work answers a question posed by Abrams and Ellis-Monaghan and provides a unified algebraic framework for studying self-twuality in combinatorial structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbits and self-twuality in set systems and delta-matroids Li, Zhuo Jin, Xian'an Yan, Qi Combinatorics We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This action extends the ribbon group framework of Abrams and Ellis-Monaghan from ribbon graphs to set systems, facilitating a systematic investigation of self-twuality. We prove that different forms of self-twuality propagate through orbits under the group action and establish a characterization of the orbit of a vf-safe delta-matroid via multimatroids. As an application, we analyze orbits of ribbon-graphic delta-matroids. Our work answers a question posed by Abrams and Ellis-Monaghan and provides a unified algebraic framework for studying self-twuality in combinatorial structures. |
| title | Orbits and self-twuality in set systems and delta-matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.15241 |