Abstract
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.