Disjoint Bases for a Countable Family of Rank-finite Matroids
نویسنده
چکیده
Let M = (Mr)reW be a system of matroids on a set S. For every transfinite sequence / of distinct elements of 5, we define a number TJ(/). In [12] we proved that the condition that r](f) 3=0 for every possible choice of/is necessary for M to have a system of mutually disjoint bases. Further, we showed that this condition is sufficient if R is countable and Mr is a rank-finite transversal matroid for every r e R. In this paper, we prove that our condition is also sufficient in the much more general case of countable systems of arbitrary rank-finite matroids.
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