Infinitesimal rigidity for non‐Euclidean bar‐joint frameworks

The minimal infinitesimal rigidity of bar‐joint frameworks in the non‐Euclidean spaces (R2,∥·∥q), for 1⩽q⩽∞,q≠2, is characterized in terms of (2,2)‐tight graphs. Specifically, a generically placed bar‐joint framework (G,p) in the plane is minimally infinitesimally rigid with respect to a non‐Euclidean ℓq norm if and only if the underlying graph G=(V,E) contains 2|V|‐2 edges and every subgraph H=(V(H),E(H)) contains at most 2|V(H)|‐2 edges.