On Disjoint Common Bases in Two Matroids
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Summary: We prove two results on packing common bases of two matroids. First, we show that the computational problem of common base packing reduces to the special case where one of the matroids is a direct sum of uniform matroids. Second, we give a counterexample to a conjecture of Chow, which proposed a sufficient condition for the existence of a common base packing. Chow's conjecture is a generalization of Rota's basis conjecture.
QA Mathematics / matematika, Combinatorial optimization, common bases, matroid intersection, Rota's conjecture, Combinatorial aspects of matroids and geometric lattices, dijoins, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), packing, Chow's conjecture
QA Mathematics / matematika, Combinatorial optimization, common bases, matroid intersection, Rota's conjecture, Combinatorial aspects of matroids and geometric lattices, dijoins, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), packing, Chow's conjecture
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