Algebraic structures on double and plane posets

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.

24 pages. Final version

References in corpus (3)

• A Self-Dual Hopf Algebra on Double Partially Ordered Sets
• Free and cofree Hopf algebras
• The infinitesimal Hopf algebra and the poset of planar forests

Cited by in corpus (2)

• Mulitgraded Dyson-Schwinger systems
• Plane posets, special posets, and permutations