Mathematics – Combinatorics
Scientific paper
2005-09-12
J. of Algebra and its Applications (8)(2009), No 4, 581--600
Mathematics
Combinatorics
22 pages; 9 figures in eps form
Scientific paper
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free. We also introduce the Hopf algebra of quasi-symmetric functions in non-commutative variables and define the product and coproduct on the monomial basis of this space and show that this Hopf algebra is free and cofree. In the process of looking for bases which generate the space we define orders on the set partitions and set compositions which allow us to define bases which have simple and natural rules for the product of basis elements.
Bergeron Nantel
Zabrocki Mike
No associations
LandOfFree
The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-2006