Triangulations, Order Polytopes, and Generalized Snake Posets

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

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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 (US)
Article number#5
JournalSeminaire Lotharingien de Combinatoire
Issue number86
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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