Work

Algebraic structures on double and plane posets

Year: 2011

Type: article

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.

DOI: 10.48550/arxiv.1101.5231

Author: Foissy, Loïc

Institutions: Laboratoire de Mathématiques de Reims, Université de Reims Champagne-Ardenne

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2953081730

FWCI: 0.449

Cites: 10

Cited by: 2

Related to: 10