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Discrete Mathematics & Theoretical Computer Science
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A combinatorial non-commutative Hopf algebra of graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 02 Jun 2014Embargo end date: 01 Jan 2013 France English Publisher:Centre pour la Communication Scientifique Directe (CCSD)Journal:Discrete Mathematics & Theoretical Computer Science, volume Vol. 16 no. 1 (eissn: 1365-8050, Copyright policy )
Authors: Duchamp, Gerard; Foissy, Loïc; Hoang-Nghia, Nguyen; Manchon, Dominique; Tanasa, Adrian;

doi: 10.46298/dmtcs.1250 , 10.48550/arxiv.1307.3928

arXiv: 1307.3928

A combinatorial non-commutative Hopf algebra of graphs

Abstract

Combinatorics 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.

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Keywords

graphs, High Energy Physics - Theory, Discrete Mathematics, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], FOS: Physical sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 510, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], High Energy Physics - Theory (hep-th), Combinatorics, discrete mathematics, combinatorics, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, noncommutative Hopf algebras, Combinatorics (math.CO), discrete scales, Mathematics

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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