Preordered forests, packed words and contraction algebras

Anthony Mansuy (1)

1 LMR - Laboratoire de Mathématiques de Reims

We introduce the notions of preordered and heap-preordered forests, generalizing the construction of ordered and heap-ordered forests. We prove that the algebras of preordered and heap-preordered forests are Hopf for the cut coproduct, and we construct a Hopf morphism to the Hopf algebra of packed words. Moreover, we define another coproduct on the preordered forests given by the contraction of edges. Finally, we give a combinatorial description of morphims defined on Hopf algebras of forests with values in the Hopf algebras of shuffes or quasi-shuffles.

Mots clés: Hopf algebra of ordered forests; quasi-shuffle algebra; Algebraic combinatorics; planar rooted trees

Domaines: Combinatoire [math.CO]

Anthony Mansuy. Preordered forests, packed words and contraction algebras. 2013. ⟨hal-00812934v2⟩