A combinatorial non-commutative Hopf algebra of graphs

作者：Duchamp Gerard H E^*; Foissy Loic; Nguyen Hoang Nghia; Manchon Dominique; Tanasa Adrian

来源：Discrete Mathematics and Theoretical Computer Science, 2014, 16(1): 355-370.

• noncommutative Hopf algebras
• graphs
• discrete scales

A non-commutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we use a quantum field theoretical (QFT) idea, namely the one of introducing discrete scales on each edge of the graph (which, within the QFT framework, corresponds to energy scales of the associated propagators). Finally, we analyze the associated quadri-coalgebra and codendrifrom structures.

• 出版日期2014