Characteristic quasi-polynomials of deletions of Shi arrangements of type C and type D
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911425291616256 |
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| author | Higashitani, Akihiro Konoike, Masato Nakashima, Norihiro Ono, Satoshi |
| author_facet | Higashitani, Akihiro Konoike, Masato Nakashima, Norihiro Ono, Satoshi |
| contents | Characteristic quasi-polynomials enumerate the number of points in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials of the restrictions of the Shi arrangements of type C and type D by one given hyperplane, respectively. The case of type C is established by extending the method developed in our previous work on type B (\cite{HN2024}), while the case of type D is deduced through a direct connection with the results on type B. As a corollary, we determine whether period collapse occurs in the characteristic quasi-polynomials of the deletions of the Shi arrangements of type C and type D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic quasi-polynomials of deletions of Shi arrangements of type C and type D Higashitani, Akihiro Konoike, Masato Nakashima, Norihiro Ono, Satoshi Combinatorics 32S22, 52C35 Characteristic quasi-polynomials enumerate the number of points in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic quasi-polynomials of the restrictions of the Shi arrangements of type C and type D by one given hyperplane, respectively. The case of type C is established by extending the method developed in our previous work on type B (\cite{HN2024}), while the case of type D is deduced through a direct connection with the results on type B. As a corollary, we determine whether period collapse occurs in the characteristic quasi-polynomials of the deletions of the Shi arrangements of type C and type D. |
| title | Characteristic quasi-polynomials of deletions of Shi arrangements of type C and type D |
| topic | Combinatorics 32S22, 52C35 |
| url | https://arxiv.org/abs/2509.02043 |