Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras

摘要

We endow the set of isomorphic classes of matroids with a new Hopf algebrastructure, in which the coproduct is implemented via the combinatorialoperations of restriction and deletion. We also initiate the investigation ofdendriform coalgebra structures on matroids and introduce a monomial invariantwhich satisfy a convolution identity with respect to restriction and deletion.