2007/11/19 by Ileana Streinu, Louis Theran, Streinu, Ileana +1
Computer Science · Mathematics · #05B35 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG) #cs.CG #math.AG #math.CO #math.MG #msc:05B35
paper · pdf · doi:10.48550/arxiv.0711.3013
Corrected some typos from the previous version; to appear in Ars Mathematica Contemporanea
arxiv created 2010/12/20 · arxiv updated 2010/12/21
A hypergraph G with n vertices and m hyperedges with d endpoints each is (k,l)-sparse if for all sub-hypergraphs G' on n' vertices and m' edges, m'≤ kn'-l. For integers k and l satisfying 0≤ l≤ dk-1, 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 (k,l)-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph G.