Algebraic structures on double and plane posets

Authors:
Loïc Foissy
Affiliations:
Laboratoire de Mathématiques, Université de Reims, Reims Cedex 2, France 51687
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2013

Citing 3
Cited 1

The infinitesimal hopf algebra and the poset of planar forests

Journal of Algebraic Combinatorics: An International Journal
A self paired Hopf algebra on double posets and a Littlewood-Richardson rule

Journal of Combinatorial Theory Series A
Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1

Deformation of the Hopf algebra of plane posets

European Journal of Combinatorics

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Abstract

We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf algebras. We also prove that they are free 2-As algebras; in particular, the Hopf algebra of posets "without N" is the free 2-As algebra on one generator. We deduce a description of the operads of 2-As algebras and of B 驴 algebras in terms of plane posets.