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 $d=r\lceil k\rceil -r+1$ functions of size (=sum of values) $k$ that are all independent in each of $r$ given matroids, there exists a rainbow set of $supp(f_i), ~i \le d$, supporting a function with the same properties.