Toric partial orders

Mike Develin, Matthew Macauley, Victor Reiner

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.

Original languageEnglish (US)
Pages (from-to)2263-2287
Number of pages25
JournalTransactions of the American Mathematical Society
Volume368
Issue number4
DOIs
StatePublished - Apr 2016

Keywords

  • Braid arrangement
  • Convex geometry
  • Coxeter element
  • Cyclic order
  • Partial order
  • Reflection functor
  • Toric arrangement
  • Transitivity
  • Unimodular

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