Volume rigidity and algebraic shifting

2022/11/01 by Bulavka, Denys, Nevo, Eran, Peled, Yuval · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.00574

Abstract

We study the generic volume rigidity of (d-1)-dimensional simplicial complexes in \mathbb R^d-1, and show that the volume rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume rigidity is \em not characterized by a corresponding hypergraph sparsity property.

Cited by

• Matroids arising from algebraic shifting
• The typical algebraic shifting of a surface
• Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach

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