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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.10236 |
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| _version_ | 1866915533359677440 |
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| author | Uchiumi, Ryo |
| author_facet | Uchiumi, Ryo |
| contents | In this paper, we introduce an equivariant version of the characteristic quasi-polynomials as the permutation characters on the complement of mod $q$ hyperplane arrangements. We prove that the permutation character is a quasi-polynomial in $q$, and show that it can be expressed by the sum of the induced characters of an equivariant version of the Ehrhart quasi-polynomials. Furthermore, we consider the case of the Coxeter arrangements, and compute in detail for type $A_\ell$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The characteristic quasi-polynomials of hyperplane arrangements with actions of finite groups Uchiumi, Ryo Combinatorics Representation Theory 05E18, 20C10, 52C35 In this paper, we introduce an equivariant version of the characteristic quasi-polynomials as the permutation characters on the complement of mod $q$ hyperplane arrangements. We prove that the permutation character is a quasi-polynomial in $q$, and show that it can be expressed by the sum of the induced characters of an equivariant version of the Ehrhart quasi-polynomials. Furthermore, we consider the case of the Coxeter arrangements, and compute in detail for type $A_\ell$. |
| title | The characteristic quasi-polynomials of hyperplane arrangements with actions of finite groups |
| topic | Combinatorics Representation Theory 05E18, 20C10, 52C35 |
| url | https://arxiv.org/abs/2508.10236 |