Tanasa, Adrian and Duchamp, Gerard and Foissy, Loïc and Hoang-Nghia, Nguyen and Manchon, Dominique - A combinatorial non-commutative Hopf algebra of graphs

dmtcs:1250 - Discrete Mathematics & Theoretical Computer Science, June 2, 2014, Vol. 16 no. 1 (in progress)
A combinatorial non-commutative Hopf algebra of graphs

Authors: Tanasa, Adrian and Duchamp, Gerard and Foissy, Loïc and Hoang-Nghia, Nguyen and Manchon, Dominique

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.


Source : oai:HAL:hal-01179226v1
Volume: Vol. 16 no. 1 (in progress)
Section: Combinatorics
Published on: June 2, 2014
Submitted on: November 29, 2013
Keywords: Discrete Mathematics, Combinatorics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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