Surfaces, Meshes, Geometric Structures — Presentations

Recent explorations of matroids with counting etc. have explored variations of the 'molecular conjecture': that certain types of geometric specialization do not reduce the generic rank of a structure. The core conjecture by Tay and Whiteley, for which a proof was just announced by Katoh and Tanigawa says that for a generically rigid (independent) body and hinge structure in 3-space with two bodies at each hinge, making all hinges of a body concurrent (polar: all coplanar) will produce a generically rigid (independent) body and hinge molecular (polar plate) framework. Here we explore k-plane matroids in connection with various related conjectures.