Hopf Algebras of Heap Ordered Trees and Permutations
arXiv:0706.1327
Abstract
It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations and show that there is a direct bialgebra isomorphism between the Hopf algebra of heap-ordered trees and the bialgebra of permutations.
10 pages LaTeX, minor revision