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

Free Quasi-symmetric Functions of Arbitrary Level

We introduce analogues of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. As applications, we recover in a simple way the descent algebras associated with wreath products Γ ≀ Sn and the corresponding generalizations of quasi-symmetric functions. Finally, we obtain Hopf algebras of colored parking functions, colored non-crossing partitions and park...

Noncommutative Symmetric Functions Iv: Quantum Linear Groups and Hecke Algebras at Q = 0

We present representation theoretical interpretations of quasi-symmetric functions and noncommutative symmetric functions in terms of quantum linear groups and Hecke algebras at q = 0. We obtain in this way a noncommutative realization of quasi-symmetric functions analogous to the plactic symmetric functions of Lascoux and Sch utzenberger.The generic case leads to a notion of quantum Schur func...

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 ...

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 ...