More on Catalan and Quasi-symmetric Functions
Last September we have discussed:
Catalan number that classically enumerate Dyck paths,
and 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
We expected the dimension of $R_n$ to be the $n$th Catalan number.
Now we can prove it all, and say even more...