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Persistent Graphs and Cyclic Polytope Triangulations
Combinatorica ( IF 1.1 ) Pub Date : 2021-02-01 , DOI: 10.1007/s00493-020-4369-5
Vincent Froese , Malte Renken

We prove a bijection between the triangulations of the 3-dimensional cyclic poly-tope C(n + 2, 3) and persistent graphs with n vertices. We show that under this bijection the Stasheff-Tamari orders on triangulations naturally translate to subgraph inclusion between persistent graphs. Moreover, we describe a connection to the second higher Bruhat order B(n, 2). We also give an algorithm to efficiently enumerate all persistent graphs on n vertices and thus all triangulations of C(n + 2, 3).



中文翻译:

持久图和循环多边三角剖分

我们证明了3维循环多拓扑Cn + 2,3)的三角剖分与具有n个顶点的持久图之间的二分性。我们表明,在这种二分法下,三角剖分的Stasheff-Tamari阶自然转换为持久图之间的子图包含。此外,我们描述了与第二个较高Bruhat阶Bn,2)的连接。我们还给出了一种算法,可以有效地枚举n个顶点上的所有持久图,从而计算出Cn + 2,3)的所有三角剖分。

更新日期:2021-02-02
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