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arXiv · 2509.02043

Characteristic quasi-polynomials of deletions of Shi arrangements of type C and type D

Akihiro Higashitani·Masato Konoike·Norihiro Nakashima·Satoshi Ono
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Abstract

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.

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Akihiro Higashitani, Masato Konoike, Norihiro Nakashima, Satoshi Ono. 2025-09-02. Characteristic quasi-polynomials of deletions of Shi arrangements of type C and type D. https://arxiv.org/abs/2509.02043

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