{TALK
{"November 2}
{"Catalan paths and Quasi-symmetric functions}
{"Nantel Bergeron}
{"York University}
{"bergeron@mathstat.yorku.ca}
{"
We investigate the quotient ring $R$ of the ring of formal power
series $\Q[[x_1,x_2,\ldots]]$ over the closure of the ideal generated
by non-constant
quasi-symmetric functions. We show that a Hilbert basis of the quotient is
naturally indexed by Catalan paths (infinite Dyck paths). We also
give a filtration of
ideals related to Catalan paths from $(0,0)$ and above the line
$y=x-k$. We investigate as well the quotient ring $R_n$ of
polynomial ring in $n$ variables over 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. [the equality is expected]
}
}