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

Authors:
Christos A. Athanasiadis
Affiliations:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395. athana@math.upenn.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1999

Citing 4
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Combinatorics of inductively factored arrangements

European Journal of Combinatorics
Intransitive trees

Journal of Combinatorial Theory Series A
Characteristic and Ehrhart Polynomials

Journal of Algebraic Combinatorics: An International Journal

Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

Journal of Algebraic Combinatorics: An International Journal

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Abstract

A hyperplane arrangement is said to satisfy the “Riemann hypothesis” if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which are defined for any irreducible root system and was proved for the root system A_n − 1. The proof is based on an explicit formula [1, 2, 11] for the characteristic polynomial, which is of independent combinatorial significance. Here our previous derivation of this formula is simplified and extended to similar formulae for all but the exceptional root systems. The conjecture follows in these cases.