Volume rigidity and algebraic shifting

Denys Bulavka; Eran Nevo; Yuval Peled

doi:10.1016/j.jctb.2024.09.002

Volume rigidity and algebraic shifting

Denys Bulavka, Eran Nevo, Yuval Peled

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in 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 not characterized by a corresponding hypergraph sparsity property.

Original language	American English
Pages (from-to)	189-202
Number of pages	14
Journal	Journal of Combinatorial Theory. Series B
Volume	170
DOIs	https://doi.org/10.1016/j.jctb.2024.09.002
State	Published - 1 Jan 2025

Keywords

Algebraic Shifting
Rigidity theory
Simplicial Complexes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2024.09.002

Cite this

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title = "Volume rigidity and algebraic shifting",

abstract = "We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−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 not characterized by a corresponding hypergraph sparsity property.",

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AU - Bulavka, Denys

AU - Nevo, Eran

AU - Peled, Yuval

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N2 - We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−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 not characterized by a corresponding hypergraph sparsity property.

AB - We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−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 not characterized by a corresponding hypergraph sparsity property.

KW - Algebraic Shifting

KW - Rigidity theory

KW - Simplicial Complexes

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DO - 10.1016/j.jctb.2024.09.002

M3 - Article

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VL - 170

SP - 189

EP - 202

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Volume rigidity and algebraic shifting

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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