Free quasi-symmetric functions, product actions and quantum field theory of partitions

Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions

Abstract. We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ ≀ Sn and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf ...

The Hopf Algebra of Non-commutative Symmetric Functions and Quasi-symmetric Functions Are Free and Cofree

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 l...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

The Hopf Algebras of Symmetric Functions and Quasisymmetric Functions in Non-commutative Variables Are Free and Cofree

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 l...

1 5 D ec 2 00 4 SYMMETRIC FUNCTIONS IN SUPERSPACE

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions , called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group acting on the sets of commuting and anticommuting variables. We first obtain superspace analogues of a number of standard obje...