Triangulations, Order Polytopes, and Generalized Snake Posets

Matias von Bell, Benjamin Braun, Derek Hanely, Khrystyna Serhiyenko, Julianne Vega, Andrés R. Vindas-Meléndezy, 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 these order polytopes and then conclude that every triangulation is 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 filters 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#5
JournalSeminaire Lotharingien de Combinatoire
Issue number86
StatePublished - 2022

Bibliographical note

Funding Information:
∗ Partially supported by the National Science Foundation under Award DMS-1953785. † Partially supported by the National Science Foundation under Award DMS-2102921.

Publisher Copyright:
© 2022, Seminaire Lotharingien de Combinatoire. All Rights Reserved.


  • generalized snake poset
  • meet-irreducible
  • order polytope
  • triangulation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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