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

Nguyen Hoang-Nghia 1 Adrian Tanasa 2, 3, 4 Christophe Tollu 1
1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 NIPNE - Horia Hulubei National Institute of Physics and Nuclear Engineering
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique
4 IUF - 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.
Keywords : dendriform coalgebras matroid polynomials matroids combinatorial Hopf algebras (CHA)
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  • HAL Id : hal-01352851, version 1

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CNRS | UNIV-BORDEAUX | LABRI | LIPN | UNIV-PARIS13 | USPC | TDS-MACS | GALILE | SORBONNE-PARIS-NORD

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Nguyen Hoang-Nghia, Adrian Tanasa, Christophe Tollu. Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.77-90. ⟨hal-01352851⟩

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