A word Hopf algebra based on the selection/quotient principle
Combinatorics
2013-09-17 v2 High Energy Physics - Theory
Abstract
In this paper, we define a Hopf algebra structure on the vector space spanned by packed words using a selection/quotient coproduct. We show that this algebra is free on its irreducible packed words. We also construct the Hilbert series of this Hopf algebra and we investigate its primitive elements.
Keywords
Cite
@article{arxiv.1207.6522,
title = {A word Hopf algebra based on the selection/quotient principle},
author = {G. H. E. Duchamp and N. Hoang-Nghia and A. Tanasa},
journal= {arXiv preprint arXiv:1207.6522},
year = {2013}
}
Comments
13 pages. Several sequences of integers found in the paper are investigated in more detail (and one of them is related to Sloane's OEIS sequence A000629). The presentation is clarified and misprints are corrected. The explanations on the choice of the name of the algebra defined in the paper are changed. Two co-authors have been added