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arXiv · 1911.05012

Persistent Graphs and Cyclic Polytope Triangulations

Vincent Froese·Malte Renken
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Abstract

We prove a bijection between the triangulations of the 3-dimensional cyclic polytope 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 additionally give an algorithm to efficiently enumerate all persistent graphs on n vertices and thus all triangulations of C(n+2, 3).

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Vincent Froese, Malte Renken. 2019-11-12. Persistent Graphs and Cyclic Polytope Triangulations. https://doi.org/10.1007/s00493-020-4369-5

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