Discrete Mathematics & Theoretical Computer Science, Vol 17, No 3 (2016)

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

Adrian Tanasa, Nguyen Hoang-Nghia, Christophe Tollu


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.

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