Catalan paths and Quasi-symmetric functions

Nantel Bergeron

York University

November 2,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

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)mathstat.yorku.ca


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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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