Triangulations, order polytopes, and generalized snake posets

Matias Von Bell, Benjamin Braun, Derek Hanely, Khrystyna Serhiyenko, Julianne Vega, Andrés R. Vindas-Meléndez, Martha Yip

Research output: Contribution to journalArticlepeer-review


This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same rank, we characterize those whose order polytopes have minimal and maximal volume. We give a combinatorial characterization of the circuits in related order polytopes and then conclude that all of their triangulations are unimodular. For a generalized snake word, we count the number of flips for the canonical triangulation of these order polytopes. We determine that the flip graph of the order polytope of the poset whose lattice of upper order ideals comes from a ladder is the Cayley graph of a symmetric group. Lastly, we introduce an operation on triangulations called twists and prove that twists preserve regular triangulations.

Original languageEnglish
Article number#10
JournalCombinatorial Theory
Issue number3
StatePublished - 2022

Bibliographical note

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  • Circuits
  • Flow polytopes
  • Order polytopes
  • Triangulations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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