Changes
New math formula: <math>\alpha \in {\mathbb Z}</math>
==Introduction==
Consider a family of sets on a finite base set and a function that takes a set from the family as input and produces an integer for output. Say, we would like to find the maximum of given function. This problem is NP-hard(the maximum clique problem can be formulated this way), but in some special cases there is a polynomial algorithm to find the optimum.
Take, for instance, a matroid <math>M</math> of rank <math>r</math> on a base set <math>S</math> where <math>|S|=2r</math>.
Suppose we arrange the base set into pairs. Should we attempt to find a base of <math>M</math> such that it contains 1 element of each given pair, we could do so via matroid intersection algorithm.
==The problem==
Find a good characterization of families of subsets of any give set where the family can be defined as the intersection of bases of a pair of matroids.
