Characteristic quasi-polynomials of ideals and signed graphs of classical root systems

Abstract

With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems ($ABCD$) with respect to the integer and root lattices. As a result, we obtain a full description of the characteristic polynomials of the toric arrangements defined by these ideals. As an application, we provide a combinatorial verification to the fact that the characteristic polynomial of every ideal subarrangement factors over the dual partition of the ideal in the classical cases.

arXiv comment17 pages, we welcome comments

References in corpus (2)

• The freeness of ideal subarrangements of Weyl arrangements
• Combinatorics of certain abelian Lie group arrangements and chromatic quasi-polynomials

Cited by in corpus (4)

• Eulerian polynomials for subarrangements of Weyl arrangements
• An equivalent formulation of chromatic quasi-polynomials
• Inductive and divisional posets
• Period collapse in characteristic quasi-polynomials of hyperplane arrangements