2012/03/08 by Jesús A. De Loera, De Loera, Jesus A., Steven Klee +1
Computer Science · Mathematics · #05E45 #52B12 #90C05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Optimization and Control (math.OC) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1203.1676
openalex publication_date 2012/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In 1980 Provan and Billera defined the notion of weak k-decomposability for pure simplicial complexes. They showed the diameter of a weakly k-decomposable simplicial complex Δ is bounded above by a polynomial function of the number of k-faces in Δ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes.