A zonotope and a product of two simplices with disconnected flip graphs

2016/05/08 by Gaku Liu, Liu, Gaku · 1 citation
Computer Science · Mathematics · #52B12 #52C45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #math.CO #math.MG #msc:52B12 #msc:52C45

paper · pdf · doi:10.48550/arxiv.1605.02366

28 pages

arxiv created 2016/05/08 · openalex publication_date 2016/05/08 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of a three-dimensional zonotope whose set of tight zonotopal tilings is not connected by flips. Using this, we show that the set of triangulations of Δ⁴ × Δⁿ is not connected by flips for large n. Our proof makes use of a non-explicit probabilistic construction.

Citations

• Flip-connectivity of triangulations of the product of a tetrahedron and simplex

Cited by

• Permutation ensembles on products of simplices

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