Comptes Rendus
Combinatoire
Algèbres de Hopf de graphes
[Hopf algebras of graphs.]
Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 607-610.

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and can be considered as generalizations of symmetric or quasi-symmetric functions.

Nous définissons des algèbres de Hopf dont les bases sont étiquetées par divers types de graphes et hypergraphes et les réalisons comme sous-algèbres d'une algèbre de polynômes en une infinité de variables. Ces algèbres sont graduées par le nombre d'arêtes et peuvent être considérées comme des généralisations des fonctions symétriques ou quasi-symétriques.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.012
Jean-Christophe Novelli 1; Jean-Yves Thibon 1; Nicolas M. Thiéry 1, 2

1 Institut Gaspard Monge, université de Marne-la-Vallée, 77454 Marne-la-Vallée cedex 2, France
2 Laboratoire de probabilités, combinatoire et statistiques, université Lyon I, bâtiment B, 50, avenue Tony-Garnier, domaine de Gerland, 69366 Lyon cedex 07, France
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Jean-Christophe Novelli; Jean-Yves Thibon; Nicolas M. Thiéry. Algèbres de Hopf de graphes. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 607-610. doi : 10.1016/j.crma.2004.09.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.012/

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