A Hopf operad of forests of binary trees and related finite-dimensional algebras

2002/09/04 by Frederic Chapoton, Chapoton, Frederic · 1 citation
Mathematics · #06A07 (Secondary) #18D50 (Primary) 05C05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C05 #msc:06A07 #msc:18D50

paper · pdf · doi:10.48550/arxiv.math/0209038

19 pages, 8 figures

arxiv created 2002/09/04 · arxiv updated 2009/11/30

Abstract

The theme of this article is the algebraic combinatorics of leaf-labeled rooted binary trees and forests of such trees. The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees. An explicit formula for the coproduct and its dual product is given, using a poset on forests.

Cited by

• On Hilbert series of Koszul operads and a classification result for set-operads

Related

• Some Hopf Algebras of Trees
• The infinitesimal Hopf algebra and the operads of planar forests
• Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
• The operads of planar forests are Koszul
• A lattice of combinatorial Hopf algebras, Application to binary trees with multiplicities