Titlebook: Rigidity and Symmetry; Robert Connelly,Asia Ivić Weiss,Walter Whiteley Book 2014 Springer Science+Business Media New York 2014 Cauchy iden

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Rigidity and Symmetry978-1-4939-0781-6Series ISSN 1069-5265 Series E-ISSN 2194-1564

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Cubic Cayley Graphs and Snarks,The well-known conjecture that there are no snarks amongst Cayley graphs is considered. Combining the theory of Cayley maps with the existence of certain kinds of independent sets of vertices in arc-transitive graphs, some new partial results are obtained suggesting promising future research directions in regards to this conjecture.

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Generic Rigidity with Forced Symmetry and Sparse Colored Graphs,We review some recent results in the generic rigidity theory of planar frameworks with forced symmetry, giving a uniform treatment to the topic. We also give new combinatorial characterizations of minimally rigid periodic frameworks with fixed-area fundamental domain and fixed-angle fundamental domain.

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Polygonal Complexes and Graphs for Crystallographic Groups,The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the classification of regular polygonal complexes, chiral polyhedra, and more generally, two-orbit polyhedra.

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Robert Connelly,Asia Ivić Weiss,Walter WhiteleyPresents state-of-the-art on the fields of rigidity and symmetry.Explores the interaction of geometry, algebra and combinatorics, presenting recent trends and advances in discrete geometry.Extends cla

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Local, Dimensional and Universal Rigidities: A Unified Gram Matrix Approach,rameworks. This PGM-based approach makes these problems amenable to semidefinite programming methodology; and naturally gives rise to results expressed in terms of Gale matrices. We survey known results emphasizing numerical examples and proofs which highlight the salient aspects of this approach.

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https://doi.org/10.1007/978-1-4939-0781-6Cauchy identity; Peterson algebras; Pieri rules; abstract polytope theory; infinite groups; rigidity theo

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