Characteristic and Ehrhart Polynomials

Authors:
Andreas Blass;Bruce E. Sagan
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1003. E-mail: ablass@umich.edu;Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027. E-mail: sagan@math.msu.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1998

Citing 6
Cited 2

Enumerative combinatorics

Enumerative combinatorics
Linear decision trees: volume estimates and topological bounds

STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Conjectures on the Quotient Ring by Diagonal Invariants

Journal of Algebraic Combinatorics: An International Journal
Subspace Arrangements of Type Bn and Dn

Journal of Algebraic Combinatorics: An International Journal
Partitions with Restricted Block Sizes, Möbius Functions, and the k-of-Each Problem

SIAM Journal on Discrete Mathematics
Graph colorings and related symmetric functions: ideas and applications1 A description of results, interesting applications, & notable open problems

Discrete Mathematics - selected papers in honor of Adriano Garsia

Extended Linial Hyperplane Arrangements for Root Systems and a Conjecture of Postnikov and Stanley

Journal of Algebraic Combinatorics: An International Journal
Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let A be a subspace arrangement and let χ(A,t) be thecharacteristic polynomial of its intersection lattice L( A). We show thatif the subspaces in A are taken from L(B_n), whereB_n is the type B Weyl arrangement, then χ(A,t) counts acertain set of lattice points. One can use this result to study the partialfactorization of χ(A,t) over the integers and the coefficients of itsexpansion in various bases for the polynomial ring R[t]. Next we prove thatthe characteristic polynomial of any Weyl hyperplane arrangement can beexpressed in terms of an Ehrhart quasi-polynomial for its affine Weylchamber. Note that our first result deals with all subspace arrangementsembedded in B_n while the second deals with all finite Weylgroups but only their hyperplane arrangements.