Anna de Mier:
Approximation and Decomposition of Clutters

There are several clutters (antichains of sets) that can be associated with matroids or other combinatorial objects, like the collection of circuits or of bases of a matroid, or the collection of minimal dominating sets of a graph. This talk is motivated by the following question: given a clutter L and a favourite family of clutters F, which clutters from F are closest to L?

We rephrase the problem in lattice theoretic terms, and characterize the families F for which there exist such closest clutters. We give algorithms to find them when F is a family that arises from matroids. We also look at the case where one requires that each of the clutters involved covers the ground set.