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 .
['Ileana Streinu', 'Louis Theran']
Natural realizations of sparsity matroids