  This article is devoted to the study of several algebras which are related to
symmetric functions, and which admit linear bases labelled by various
combinatorial objects: permutations (free quasi-symmetric functions), standard
Young tableaux (free symmetric functions) and packed integer matrices (matrix
quasi-symmetric functions). Free quasi-symmetric functions provide a kind of
noncommutative Frobenius characteristic for a certain category of modules over
the 0-Hecke algebras. New examples of indecomposable $H_n(0)$-modules are
discussed, and the homological properties of $H_n(0)$ are computed for small
$n$. Finally, the algebra of matrix quasi-symmetric functions is interpreted as
a convolution algebra.
