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HOPF ALGEBRAS OF DIAGRAMS

Institut Galilée, LIPN, CNRS UMR 7030, 99, Avenue J.-B. Clement, F-93430 Villetaneuse, France

LITIS, Université de Rouen; Avenue de l'université, 76801 Saint Étienne du Rouvray, France

Université Paris-Est, Institut Gaspard Monge, 5 Boulevard Descartes, Champs-Sur-Marne, 77454 Marne-la-Vallée Cedex 2, France

Corresponding author.

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C. TOLLU

Institut Galilée, LIPN, CNRS UMR 7030, 99, Avenue J.-B. Clement, F-93430 Villetaneuse, France

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F. TOUMAZET

Université Paris-Est, Institut Gaspard Monge, 5 Boulevard Descartes, Champs-Sur-Marne, 77454 Marne-la-Vallée Cedex 2, France

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https://doi.org/10.1142/S0218196711006418Cited by:1 (Source: Crossref)

Abstract

We investigate several generalizations of the Hopf algebra MQSym whose constructions come from labelings of special diagrams in bijection with packed matrices. Their products come either from the Hopf algebras WSym or WQSym, respectively built on integer set partitions and set compositions. Realizations on bi-word are exhibited, and it is shown how these algebras fit into a commutative diagram. Hopf deformations and dendriform structures are also considered for some algebras in the picture.

Keywords:

AMSC: Primary 05E99, Secondary 16W30, Secondary 18D50

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