arXiv subjects
Publications and source records attributed to R. L. Grossman.
Description of cocommutative Hopf algebras associated with families of trees. Applications include Cayley's theorem on the number of rooted trees with n nodes, and Catalan's theorem on the number of rooted ordered trees with n nodes.
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.