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Discrete Mathematics & Theoretical Computer Science |
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 : ScholeXplorer
IsRelatedTo ARXIV 0802.0791 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s00220-008-0658-3 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0802.0791 Source : ScholeXplorer IsRelatedTo HANDLE 21.11116/0000-0004-25BF-C Source : ScholeXplorer IsRelatedTo HANDLE 21.11116/0000-0004-25C1-8
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