2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141977It 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 revisionRings and Algebras16W30text