Nguyen Hoang-Nghia ; Adrian Tanasa ; Christophe Tollu - Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras

dmtcs:2157 - Discrete Mathematics & Theoretical Computer Science, February 26, 2016, Vol. 17 no. 3 - https://doi.org/10.46298/dmtcs.2157
Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras

Authors: Nguyen Hoang-Nghia 1; Adrian Tanasa ORCID-iD2,3,4; Christophe Tollu 1

  • 1 Laboratoire d'Informatique de Paris-Nord
  • 2 Horia Hulubei National Institute of Physics and Nuclear Engineering
  • 3 Laboratoire Bordelais de Recherche en Informatique
  • 4 Institut Universitaire de France

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.

https://doi.org/10.46298/dmtcs.2157
Source: HAL:hal-01352851v1
Volume: Vol. 17 no. 3
Section: Combinatorics
Published on: February 26, 2016
Submitted on: October 13, 2014
Keywords: dendriform coalgebras, matroid polynomials,matroids, combinatorial Hopf algebras (CHA),[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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Source : ScholeXplorer IsRelatedTo ARXIV math/0505207
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jpaa.2006.06.005
  • 10.1016/j.jpaa.2006.06.005
  • math/0505207
Bidendriform bialgebras, trees, and free quasi-symmetric functions

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