Morphisms and order ideals of toric posets

TL;DR

This paper explores the structure of toric posets, focusing on their intervals, morphisms, and order ideals, and connects these concepts to cyclic reducibility and conjugacy in Coxeter groups.

Contribution

It introduces new concepts of toric intervals, morphisms, and order ideals, and establishes their relationship with Coxeter group properties.

Findings

Defined toric intervals, morphisms, and order ideals.

Connected toric poset structures to Coxeter group cyclic reducibility.

Provided new combinatorial and geometric insights into toric posets.

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.