Generic Symmetry-Forced Infinitesimal Rigidity: Translations and Rotations

DOI10.1137/20M1346961zbMath1487.52028arXiv2003.10529MaRDI QIDQ5073710

Daniel Irving Bernstein

Publication date: 3 May 2022

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.10529

zbMATH Keywords

rotationrigid graphstranslationtropical geometrymatroid theorysymmetry-forced rigidity

Mathematics Subject Classification ID

Geometric aspects of tropical varieties (14T20) Combinatorial aspects of matroids and geometric lattices (05B35) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25)

Related Items

The first-order flexibility of a crystallographic framework

Uses Software

• LamanGraphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gain-sparsity and symmetry-forced rigidity in the plane
• Infinite bar-joint frameworks, crystals and operator theory
• Algebraic matroids and set-theoretic realizability of tropical varieties
• An implicitization challenge for binary factor analysis
• The orbit rigidity matrix of a symmetric framework
• Biased graphs. I: Bias, balance, and gains
• Frameworks with forced symmetry. I: Reflections and rotations
• Hadamard products of linear spaces
• Elimination theory for tropical varieties
• Simultaneous static and kinematic indeterminacy of space trusses with cyclic symmetry
• The rigidity of graphs. II
• Biased graphs. II: The three matroids
• An algorithm for two-dimensional rigidity percolation: The pebble game
• Minkowski sums and Hadamard products of algebraic varieties
• The Hilbert function of some Hadamard products
• On the determinacy of repetitive structures.
• Symmetry and states of self-stress in triangulated toroidal frames.
• Group symmetry in interior-point methods for semidefinite program
• The number of embeddings of minimally rigid graphs
• Generic combinatorial rigidity of periodic frameworks
• Lifting tropical intersections
• Hadamard star configurations
• On the Hadamard product of degenerate subvarieties
• Inductive constructions for frameworks on a two-dimensional fixed torus
• Frameworks with forced symmetry. II: Orientation-preserving crystallographic groups
• Computing tropical varieties
• Crystal frameworks, symmetry and affinely periodic flexes
• Submodular functions and independence structures
• On graphs and rigidity of plane skeletal structures
• Periodic frameworks and flexibility
• Matroids of gain graphs in applied discrete geometry
• On Generic Rigidity in the Plane
• The Rigidity of Graphs
• The Number of Realizations of a Laman Graph
• A Generalisation of the Matroid Lift Construction
• On Hadamard products of linear varieties
• Stable intersections of tropical varieties