Terrain Visibility Graphs and Cyclic Polytope Triangulations

11/12/2019

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by   Vincent Froese, et al.

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