Volume rigidity and algebraic shifting

Denys Bulavka; Eran Nevo; Yuval Peled

Volume rigidity and algebraic shifting

Denys Bulavka, Eran Nevo, Yuval Peled

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	English
Article number	#14
Journal	Seminaire Lotharingien de Combinatoire
Issue number	89
State	Published - 1 Jan 2023
Externally published	Yes

Keywords

algebraic shifting
exterior algebra
rigidity

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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.",

keywords = "algebraic shifting, exterior algebra, rigidity",

author = "Denys Bulavka and Eran Nevo and Yuval Peled",

year = "2023",

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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 - exterior algebra

KW - rigidity

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M3 - Article

AN - SCOPUS:85181972319

SN - 1286-4889

JO - Seminaire Lotharingien de Combinatoire

JF - Seminaire Lotharingien de Combinatoire

IS - 89

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Volume rigidity and algebraic shifting

Abstract

Keywords

ASJC Scopus subject areas

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