## Catalan Paths and Quasi-symmetric Functions

**Nantel Bergeron**

(York University)

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
above by

the $n$th Catalan number. [In fact the equality should hold]