Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910037107015680 |
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| author | Mori, Yusuke Nakashima, Norihiro |
| author_facet | Mori, Yusuke Nakashima, Norihiro |
| contents | Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials for specific arrangements which contain the Coxeter arrangements of types A, B, C, and D described by the orthonormal basis. We also compute the characteristic quasi-polynomials for their deletion arrangements and we can show that they are factorized. From this result, the poset generated by hypertori of the corresponding toric arrangement is an inductive poset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00735 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D Mori, Yusuke Nakashima, Norihiro Combinatorics 32S22 (Primary) 52C35 (Secondary) Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials for specific arrangements which contain the Coxeter arrangements of types A, B, C, and D described by the orthonormal basis. We also compute the characteristic quasi-polynomials for their deletion arrangements and we can show that they are factorized. From this result, the poset generated by hypertori of the corresponding toric arrangement is an inductive poset. |
| title | Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D |
| topic | Combinatorics 32S22 (Primary) 52C35 (Secondary) |
| url | https://arxiv.org/abs/2208.00735 |