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.
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.
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@article{CRMATH_2004__339_9_607_0,
author = {Novelli, Jean-Christophe and Thibon, Jean-Yves and Thi\'ery, Nicolas M.},
title = {Alg\`ebres de {Hopf} de graphes},
journal = {Comptes Rendus. Math\'ematique},
pages = {607--610},
publisher = {Elsevier},
volume = {339},
number = {9},
year = {2004},
doi = {10.1016/j.crma.2004.09.012},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.09.012/}
}
TY - JOUR AU - Novelli, Jean-Christophe AU - Thibon, Jean-Yves AU - Thiéry, Nicolas M. TI - Algèbres de Hopf de graphes JO - Comptes Rendus. Mathématique PY - 2004 SP - 607 EP - 610 VL - 339 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.09.012/ DO - 10.1016/j.crma.2004.09.012 LA - fr ID - CRMATH_2004__339_9_607_0 ER -
%0 Journal Article %A Novelli, Jean-Christophe %A Thibon, Jean-Yves %A Thiéry, Nicolas M. %T Algèbres de Hopf de graphes %J Comptes Rendus. Mathématique %D 2004 %P 607-610 %V 339 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.09.012/ %R 10.1016/j.crma.2004.09.012 %G fr %F CRMATH_2004__339_9_607_0
Novelli, Jean-Christophe; Thibon, Jean-Yves; Thiéry, Nicolas M. Algèbres de Hopf de graphes. Comptes Rendus. Mathématique, Tome 339 (2004) no. 9, pp. 607-610. doi : 10.1016/j.crma.2004.09.012. http://www.numdam.org/articles/10.1016/j.crma.2004.09.012/
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