Hopf Algebras of Heap Ordered Trees and Permutations

TL;DR

This paper establishes a new algebraic structure on permutations and demonstrates an isomorphism with the existing Hopf algebra of heap-ordered trees, deepening the understanding of their algebraic relationships.

Contribution

It introduces a new bialgebra structure on permutations and proves a direct isomorphism with the Hopf algebra of heap-ordered trees.

Findings

New bialgebra structure on permutations

Isomorphism between permutation bialgebra and heap-ordered trees

Enhanced understanding of algebraic relationships

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.