稀疏拟阵的自然实现
Natural realizations of sparsity matroids
摘要：
具有n个顶点和m条超边的超图G是（k，l）-稀疏的，如果对所有n'个顶点和m'条边的子超图G'，m' \le kn '-1.对于满足0 \le 1 \le dk-1的整数k和l，已知这是一个线性可表示拟阵族。受刚性理论问题的启发，我们给出了（k，l）-稀疏超图的一个新的线性表示定理，即，表示矩阵捕捉底层超图G的顶点边关联结构。
英文摘要：
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'\le kn'-l. For integers k and l satisfying 0\le l\le 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
