A combinatorial characterization of generic infinitesimal rigidity for frameworks in any Euclidean dimension is given using Plücker relations on the Grassmannian and Young's straightening law on tableaux.
John, Stephanie Stark, Louis Theran, and Xilin Yu
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Generic Rigidity of Graph Frameworks in Euclidean Space
A combinatorial characterization of generic infinitesimal rigidity for frameworks in any Euclidean dimension is given using Plücker relations on the Grassmannian and Young's straightening law on tableaux.