Persistent Graphs and Cyclic Polytope Triangulations
Discrete Mathematics
2021-02-17 v2 Combinatorics
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).
Keywords
Cite
@article{arxiv.1911.05012,
title = {Persistent Graphs and Cyclic Polytope Triangulations},
author = {Vincent Froese and Malte Renken},
journal= {arXiv preprint arXiv:1911.05012},
year = {2021}
}