Morphisms and order ideals of toric posets
arXiv:1501.02239
Abstract
Toric posets are cyclic analogues of finite posets. They can be viewed combinatorially as equivalence classes of acyclic orientations generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane arrangements. In this paper we study toric intervals, morphisms, and order ideals, and we provide a connection to cyclic reducibility and conjugacy in Coxeter groups.
28 pages, 8 figures. A 12-page "extended abstract" version appears as [v2]