Morphisms and Order Ideals of Toric Posets

Matthew Macauley
Additional contact information
Matthew Macauley: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA

Mathematics, 2016, vol. 4, issue 2, 1-31

Abstract: Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements. They can be thought of combinatorially as equivalence classes of acyclic orientations under the equivalence relation generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane arrangements. In this paper, we define toric intervals and toric order-preserving maps, which lead to toric analogues of poset morphisms and order ideals. We develop this theory, discuss some fundamental differences between the toric and ordinary cases, and outline some areas for future research. Additionally, we provide a connection to cyclic reducibility and conjugacy in Coxeter groups.

Keywords: Coxeter group; cyclic order; cyclic reducibility; morphism; partial order; preposet; order ideal; order-preserving map; toric hyperplane arrangement; toric poset; 06A06, 52C35 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/4/2/39/pdf (application/pdf)
https://www.mdpi.com/2227-7390/4/2/39/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:4:y:2016:i:2:p:39-:d:71469

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().