(2) Horia Hulubei National Institute of Physics and Nuclear Engineering
(3) Laboratoire Bordelais de Recherche en Informatique
(4) Institut Universitaire de France
(5) Institut universitaire de France
Abstract
We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion. We also initiate the investigation of dendriform coalgebra structures on matroids and introduce a monomial invariant which satisfy a convolution identity with respect to restriction and deletion.
