Preordered forests, packed words and contraction algebras
Combinatorics
2013-05-03 v1
Abstract
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.
Cite
@article{arxiv.1305.0343,
title = {Preordered forests, packed words and contraction algebras},
author = {Anthony Mansuy},
journal= {arXiv preprint arXiv:1305.0343},
year = {2013}
}
Comments
42 pages. arXiv admin note: text overlap with arXiv:1007.1547, arXiv:1004.5208 by other authors