Natural realizations of sparsity matroids

Authors: Ileana Streinu and Louis Theran
Journal: Ars Mathematica Contemporanea, 41, 2011.
Full text: arXiv

A hypergraph with vertices and hyperedges with endpoints each is -sparse if for all sub-hypergraphs on vertices and edges, . For integers and satisfying , this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the -sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph .