Combinatorics of certain abelian Lie group arrangements and chromatic quasi-polynomials

Abstract

The purpose of this paper is twofold. Firstly, we generalize the notion of characteristic polynomials of hyperplane and toric arrangements to those of certain abelian Lie group arrangements. Secondly, we give two interpretations for the chromatic quasi-polynomials and their constituents through subspace and toric viewpoints.

16 pages

References in corpus (2)

• Affine and toric hyperplane arrangements
• Mobius Conjugation and Convolution Formulae

Cited by in corpus (8)

• Characteristic quasi-polynomials of ideals and signed graphs of classical root systems
• Eulerian polynomials for subarrangements of Weyl arrangements
• An equivalent formulation of chromatic quasi-polynomials
• Set of independencies and Tutte polynomial of matroids over a domain
• Poincaré polynomial of elliptic arrangements is not a specialization of the Tutte polynomial
• Inductive and divisional posets
• Period collapse in characteristic quasi-polynomials of hyperplane arrangements
• Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D