On Greedy Bases Packing in Matroids

Let S be a finite set and M = (S, B) be a matroid where B is the set of its bases. We say that a basis B is greedy in M or the pair (M, B) is greedy if, for every sum of bases vector w, the coefficient:λ(B, w) = max{λ ≥ 0 : w − λBisagainasumofbasesvector }, where B and its characteristic vector will not be distinguished, is integer. We define a notion of minors for (M, B) pairs and we give a characterization of greedy pairs by excluded minors. This characterization gives a large class of matroids for which an integer Carathéodory’s theorem is true.