Choice functions in the intersection of matroids
Abstract
We prove a common generalization of two results, one on rainbow fractional matchings and one on rainbow sets in the intersection of two matroids: Given d = r k - r + 1 functions of size (=sum of values) k that are all independent in each of r given matroids, there exists a rainbow set of supp(fi), i ≤ d, supporting a function with the same properties.
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