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arXiv · 2208.00735

Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D

Yusuke Mori·Norihiro Nakashima
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Abstract

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.

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Yusuke Mori, Norihiro Nakashima. 2022-08-01. Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D. https://doi.org/10.1007/s11083-026-09726-3

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