Catalan Paths and Quasi-symmetric Functions
Catalan number classically enumerate Dyck paths.
We investigate the quotient ring $R_n$ of the ring of polynomials
$\Q[[x_1,x_2,\ldots,x_n]]$ over the the ideal generated by non-constant
quasi-symmetric polynomials. We show that the dimension of $R_n$ is bounded
the $n$th Catalan number. [In fact the equality should hold]