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Discrete Mathematics & Theoretical Computer Science |
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.2157Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebrasArticle
Authors: Nguyen Hoang-Nghia 1; Adrian Tanasa 
2,3,4,5; Christophe Tollu 1
- 1 Laboratoire d'Informatique de Paris-Nord
- 2 Horia Hulubei National Institute of Physics and Nuclear Engineering [IUF]
- 3 Laboratoire Bordelais de Recherche en Informatique
- 4 Institut Universitaire de France
- 5 Institut universitaire de France [IUF]
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.
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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