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arxiv: 0812.3407 · v1 · submitted 2008-12-17 · 🧮 math.CO

Hopf Algebras of Graphs

Jean-Christophe Novelli (1) , Jean-Yves Thibon (1) , Nicolas M. Thi\'ery (2) ((1) Institut Gaspard Monge , Universit\'e de Marne-la-Vall\'ee , France (2) Laboratoire de Probabilit\'es , Combinatoire et Statistiques , Universit\'e Claude Bernard Lyon I , France) This is my paper
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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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