Geodesic
A Word Hopf Algebra Based on the Selection/Quotient Principle
Séminaire lotharingien de combinatoire, Tome 68 (2012-2013)

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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 compute the Hilbert series of this Hopf algebra, and we investigate its primitive elements. 

@article{SLC_2012-2013_68_a2,
     author = {G\'erard H. E. Duchamp and Nguyen Hoang-Nghia and Adrian Tanasa},
     title = {A {Word} {Hopf} {Algebra} {Based} on the {Selection/Quotient} {Principle}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {68},
     year = {2012-2013},
     url = {http://geodesic.mathdoc.fr/item/SLC_2012-2013_68_a2/}
}
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Gérard H. E. Duchamp; Nguyen Hoang-Nghia; Adrian Tanasa. A Word Hopf Algebra Based on the Selection/Quotient Principle. Séminaire lotharingien de combinatoire, Tome 68 (2012-2013). http://geodesic.mathdoc.fr/item/SLC_2012-2013_68_a2/