Catalan paths and Quasi-symmetric functions

Nantel Bergeron

York University

October 19,
refreshments at 3:45pm


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]

Speaker's Contact Info: bergeron(at-sign)

Return to seminar home page

Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

Page loaded on September 26, 2001 at 11:09 AM. Copyright © 1998-99, Sara C. Billey. All rights reserved.