The Bernoulli basis construction for the extended Shi and Catalan arrangements of the type Al−1
Abstract
The cones over the extended Shi and Catalan arrangements are known to be free. In this paper, we provide an explicit construction of bases for the extended Shi and Catalan arrangements of type Al−1 using Bernoulli polynomials, we refer to these as the Bernoulli bases. Our construction generalizes the case of Shi arrangement studied by D. Suyama and H. Terao. Moreover, we rigorously establish the relationship between the Bernoulli bases and the integral bases introduced by D. Suyama and M. Yoshinaga.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Commutative Algebra and Its Applications
Advanced Algebra and Geometry
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–14
- Publication date
- 19 January 2026
- Language
- EN