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4 papers · 2 filters
The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree
Nantel Bergeron, Mike Zabrocki
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 th…
Posets related to the connectivity set of Coxeter groups
Nantel Bergeron, Christophe Hohlweg, Mike Zabrocki
We define the notion of connectivity set for elements of any finitely generated Coxeter group. Then we define an order related to this new statistic and show that the poset is grad…
On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia
M. H. Albert, M. Elder, A. Rechnitzer +2
We construct a sequence of finite automata that accept subclasses of the class of 4231-avoiding permutations. We thereby show that the Wilf-Stanley limit for the class of 4231-avoi…
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
Nantel Bergeron, Christophe Reutenauer, Mercedes Rosas +1
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this…