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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.10838 |
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| _version_ | 1866914195545522176 |
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| author | Kuroda, Masamichi Nakashima, Norihiro Tsujie, Shuhei |
| author_facet | Kuroda, Masamichi Nakashima, Norihiro Tsujie, Shuhei |
| contents | The characteristic polynomial plays an important role in study of hyperplane arrangements. There are several refinements of the characteristic polynomial. One of them is the coboundary polynomial defined by Crapo. Another refinement is the characteristic quasi-polynomial for an integral arrangement defined by Kamiya, Takemura, and Terao. Recently, the first and third authors introduced the characteristic quasi-polynomial for arrangement defined over a residually finite Dedekind domain. In this article, we introduce the common refinement of the coboundary polynomial and characteristic quasi-polynomial for an arrangement over a residually finite Dedekind domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Coboundary Quasi-Polynomials of Hyperplane Arrangements over Residually Finite Dedekind Domains Kuroda, Masamichi Nakashima, Norihiro Tsujie, Shuhei Combinatorics 52C35, 05E40 The characteristic polynomial plays an important role in study of hyperplane arrangements. There are several refinements of the characteristic polynomial. One of them is the coboundary polynomial defined by Crapo. Another refinement is the characteristic quasi-polynomial for an integral arrangement defined by Kamiya, Takemura, and Terao. Recently, the first and third authors introduced the characteristic quasi-polynomial for arrangement defined over a residually finite Dedekind domain. In this article, we introduce the common refinement of the coboundary polynomial and characteristic quasi-polynomial for an arrangement over a residually finite Dedekind domain. |
| title | The Coboundary Quasi-Polynomials of Hyperplane Arrangements over Residually Finite Dedekind Domains |
| topic | Combinatorics 52C35, 05E40 |
| url | https://arxiv.org/abs/2512.10838 |