New recursion formula for the interior polynomial based on non-expanding sets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916773582864384 |
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| author | Kato, Keiju |
| author_facet | Kato, Keiju |
| contents | The interior polynomial was originally defined for hypergraphs and later shown to coincide with the Ehrhart polynomial of the root polytope of an associated bipartite graph. In previous work, we derived an alternating cycle recursion formula for the interior polynomial. Here, we introduce a new, more transparent recursion formula based on the structure of non-expanding sets. This formula offers a clearer combinatorial interpretation of the interior polynomial and its connection to polyhedral geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New recursion formula for the interior polynomial based on non-expanding sets Kato, Keiju Combinatorics Geometric Topology 05C31, 05C10, 52B05, 57K14, 57M15 The interior polynomial was originally defined for hypergraphs and later shown to coincide with the Ehrhart polynomial of the root polytope of an associated bipartite graph. In previous work, we derived an alternating cycle recursion formula for the interior polynomial. Here, we introduce a new, more transparent recursion formula based on the structure of non-expanding sets. This formula offers a clearer combinatorial interpretation of the interior polynomial and its connection to polyhedral geometry. |
| title | New recursion formula for the interior polynomial based on non-expanding sets |
| topic | Combinatorics Geometric Topology 05C31, 05C10, 52B05, 57K14, 57M15 |
| url | https://arxiv.org/abs/2502.19799 |