{"content":[{"text":"Also available at http://amc-journal.eu \n ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.) \n Ars Mathematica Contemporanea Volume 4, Issue 1, Year 2011, Pages 141-151","bbox":{"left":0.121992,"top":0.188707,"width":0.756101,"height":0.06030199999999997}},{"text":"Natural realizations of sparsity matroids","bbox":{"left":0.237889,"top":0.276164,"width":0.523987,"height":0.029611}},{"text":"Ileana Streinu, Louis Theran","bbox":{"left":0.326984,"top":0.324753,"width":0.34595899999999996,"height":0.02852100000000002}},{"text":"Abstract","bbox":{"left":0.118968,"top":0.374546,"width":0.112417,"height":0.029611}},{"text":"A hypergraph G with n vertices and m hyperedges with d \n endpoints each is (k, l)-sparse if for all subhypergraphs G' on n' \n vertices and m' edges, m' ≤ kn' − l. For integers k and l satisfying \n 0 ≤ l ≤ dk − 1, this is known to be a linearly representable \n matroidal family. Motivated by problems in rigidity theory, we \n give a new linear representation theorem for the (k, l)-sparse \n hypergraphs that is natural; i.e., the representing matrix \n captures the vertex-edge incidence structure of the underlying \n hypergraph G.","bbox":{"left":0.118968,"top":0.4231,"width":0.762272,"height":0.22509399999999996}},{"text":"Keywords: Matroids, combinatorial rigidity, sparse graphs and \n hypergraphs.","bbox":{"left":0.118968,"top":0.668847,"width":0.761927,"height":0.05317800000000006}},{"text":"Math. Subj. Class.: 52C25, 05B35, 05C65, 68R10","bbox":{"left":0.118968,"top":0.742679,"width":0.605986,"height":0.02851999999999999}},{"text":"Math Sci Net: 05B35 (05C65 52B40 68R10)","bbox":{"left":0.118968,"top":0.791888,"width":0.543725,"height":0.02851999999999999}}],"images_bbox":[{"left":0.123161,"top":0.110889,"width":0.102612,"height":0.042052},{"left":0.665188,"top":0.114168,"width":0.168514,"height":0.039481}],"images_bbox_not_text_overlap":[{"left":0.123161,"top":0.110889,"width":0.102612,"height":0.042052},{"left":0.665188,"top":0.114168,"width":0.168514,"height":0.039481}]}