Abstract and Generic Rigidity in the Plane

AND GENERIC RIGIDITY IN THE PLANE SACHIN PATKAR, BRIGITTE SERVATIUS, AND K. V. SUBRAHMANYAM Abstract. We consider the concept of abstract 2–dimensional rigidity and provide necessary and sufficient conditions for a matroid to be an abstract rigidity matroid of a complete graph. This characterization is a natural extenWe consider the concept of abstract 2–dimensional rigidity and provide necessary and sufficient conditions for a matroid to be an abstract rigidity matroid of a complete graph. This characterization is a natural extension of the characterization of graphic matroids due to Graver or Sachs. We also give an example of an abstract rigidity matroid which is not infinitesimal.