Motions of grid-like reflection frameworks. (September 2018)

• Record Type: Journal Article
• Authors: Kitson, D.; Schulze, B.
• Is Part Of: Journal of symbolic computation. Volume 88(2018)
• Page Start: 47
• Page End: 66
• Publication Date: 2018-09
• Subjects: 52C25 -- 05C50; Bar-joint framework -- Infinitesimal rigidity -- Non-Euclidean rigidity -- Orbit matrix -- Signed graph -- Sparsity counts; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.02.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the reflection acts freely on the vertex set. At the framework level, these characterisations are given in terms of induced monochrome subgraph decompositions, and at the graph level they are given in terms of sparsity counts and recursive construction sequences for the corresponding signed quotient graphs.