Affordable Access

Publisher Website

Irreducible circuits and Coxeter arrangements

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
114
Issue
7
Identifiers
DOI: 10.1016/j.jcta.2007.01.005
Keywords
  • Oriented Matroid
  • Vector Arrangement
  • Root System

Abstract

Abstract We introduce the concept of irreducible circuits. In a vector arrangement Φ, these are configurations consisting of one vector α ∈ Φ in the positive linear span of an independent set Δ ⊂ Φ such that no proper subset of Δ has any member of Φ − Δ in its positive linear span. We show that the oriented matroid of any centrally symmetric vector arrangement is constructively determined by its irreducible circuits, and classify the irreducible circuits in root systems.

There are no comments yet on this publication. Be the first to share your thoughts.