Triangulations, Order Polytopes, and Generalized Snake Posets
Triangulations, Order Polytopes, and Generalized Snake Posets
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DOI：
10.5070/c62359166
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
Matias von Bell;Benjamin Braun;Derek Hanely;K. Serhiyenko;Julianne Vega;Andr'es R. Vindas-Mel'endez;Martha Yip
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作者：
Matias von Bell;Benjamin Braun;Derek Hanely;K. Serhiyenko;Julianne Vega;Andr'es R. Vindas-Mel'endez;Martha Yip
本文研究了由广义蛇偏序集及其交不可约元偏序集所产生的序多面体。在同秩的广义蛇偏序集中，我们刻画了那些序多面体具有最小和最大体积的偏序集。我们给出了这些序多面体中的电路的组合特征，然后得出结论，每个正则三角剖分是么模的。对于一个广义的蛇字，我们计数的翻转这些顺序多面体的规范三角剖分的数量。我们确定了滤子格来自于梯子的偏序集的序多面体的翻转图是对称群的Cayley图。最后，我们介绍了三角剖分的一个操作称为扭曲，并证明扭曲保持定期三角剖分。
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 regular 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.