Free Quasi-symmetric Functions of Arbitrary Level

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

Inversion of some series of free quasi-symmetric functions

The algebra of Free Quasi-Symmetric Functions FQSym [5] is a graded algebra of noncommutative polynomials whose bases are parametrized by permutations. Under commutative image, it is mapped onto Gessel’s algebra of quasi-symmetric functions, whence its name. Quasi-symmetric functions generalize symmetric functions in a natural way, and many classical results admit quasi-symmetric extensions or ...

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 algebraic combinatorics of snakes

Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main purpose is to show that several properties of the generating functions of snakes, such as differential equations or closed form as trigonometric functions, can ...

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

This article is essentially an appendix to [4]. We gather here some useful properties of the algebra FQSym of free quasi-symmetric functions which were overlooked in [4]. Recall that FQSym is a subalgebra of the algebra of noncommutative polynomials in infinitely many variables ai which is mapped onto Gessel’s algebra of quasi-symmetric functions QSym by the commutative image ai 7→ xi of K〈A〉. ...