Preordered forests, packed words and contraction algebras

JOURNAL OF ALGEBRA

卷:411

Article

Mansuy, Anthony

关键词: Algebraic combinatorics;    Planar rooted trees;    Hopf algebra of ordered forests;    Quasi-shuffle algebra;   

DOI  :  10.1016/j.jalgebra.2014.04.017

来源: Elsevier

【 摘 要 】

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 morphism defined on Hopf algebras of forests with values in the Hopf algebras of shuffles or quasi-shuffles. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free