Cumulants, lattice paths, and orthogonal polynomials

A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants.Comment: 11 pages, AMS LaTeX, uses pstricks; revised according to referee's suggestions, in particular cut down last section and corrected some wrong attribution

Noncommutative Symmetric Functions Associated with a Code, Lazard Elimination, and Witt Vectors

The construction of the universal ring of Witt vectors is related to Lazard's factorizations of free monoids by means of a noncommutative analogue. This is done by associating to a code a specialization of noncommutative symmetric functions

Multiple orthogonal polynomials, d-orthogonal polynomials, production matrices, and branched continued fractions

I analyze an unexpected connection between multiple orthogonal polynomials, d-orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot's combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal

Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization

In this work, an effective construction, via Sch\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed