Séminaire Lotharingien de Combinatoire, 89B.4 (2023), 12 pp.
Nicholas J. Williams
Studying Triangulations of Even-Dimensional Cyclic Polytopes via Directed Graphs
Abstract.
We prove two results on triangulations of even-dimensional cyclic polytopes using the directed graphs (digraphs) implicitly associated to them by Oppermann and Thomas. First, we show that the digraph of a 2d-dimensional triangulation encodes whether or not the triangulation has an interior (d+1)-simplex, and we describe the digraphs of such triangulations. Secondly, we show that the digraph of the triangulation allows one to identify the internal d-simplices which admit bistellar flips. This also allows one to easily compute the outcome of a bistellar flip.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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