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

TL;DR

This paper extends the concept of characteristic polynomials to abelian Lie group arrangements and offers two interpretations of chromatic quasi-polynomials from subspace and toric perspectives.

Contribution

It introduces a generalization of characteristic polynomials for abelian Lie group arrangements and provides dual interpretations of chromatic quasi-polynomials.

Findings

Generalized characteristic polynomials for abelian Lie group arrangements

Two interpretations of chromatic quasi-polynomials from different viewpoints

Enhanced understanding of the combinatorial structure of arrangements

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.