Catalan numbers and Schubert polynomials for $w=1(n+1)...2$

Abstract

We show that the Schubert polynomial S_w specializes to the Catalan number C_n when $w=1(n+1)...2$. Several proofs of this result as well as a q-analog are given. An application to the singularities of Schubert varieties is given.

9 pages, 1 figure

References in corpus (1)

• Multiplicities of the Most Singular Point on Schubert varieties on Gl(n)/B for n=5,6