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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.11283 |
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| _version_ | 1866916769966325760 |
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| author | Lotter, Felix Preiß, Rosa |
| author_facet | Lotter, Felix Preiß, Rosa |
| contents | The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial automorphisms of the polytope. Motivated by this observation, we look for other linear combinations of iterated integrals that are invariant under the subgroup action. This yields interesting polynomial attributes of the cyclic polytope. We prove that there are infinitely many of these invariants which are algebraically independent in the shuffle algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclic polytopes through the lens of iterated integrals Lotter, Felix Preiß, Rosa Rings and Algebras Combinatorics 60L10, 13A50, 52B05 The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial automorphisms of the polytope. Motivated by this observation, we look for other linear combinations of iterated integrals that are invariant under the subgroup action. This yields interesting polynomial attributes of the cyclic polytope. We prove that there are infinitely many of these invariants which are algebraically independent in the shuffle algebra. |
| title | Cyclic polytopes through the lens of iterated integrals |
| topic | Rings and Algebras Combinatorics 60L10, 13A50, 52B05 |
| url | https://arxiv.org/abs/2412.11283 |