Algebraic structures on double and plane posets

2011/01/27 by Loïc Foissy, Foissy, Loïc · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1101.5231

openalex publication_date 2011/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_infty algebras in terms of plane posets.

Citations

• Les algebres de Hopf des arbres enracines decores
• Free and cofree Hopf algebras

Cited by

• Mulitgraded Dyson-Schwinger systems

Related

• Plane posets, special posets, and permutations
• Surjections and double posets
• Deformation of the Hopf algebra of plane posets
• Combinatorial Hopf algebras
• Free and cofree Hopf algebras