## Li, Nan - Product of Stanley symmetric functions

dmtcs:3064 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Product of Stanley symmetric functions

Authors: Li, Nan

We study the problem of expanding the product of two Stanley symmetric functions $F_w·F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_w=\lim _n→∞\mathfrak{S}_{1^n×w}$, and study the behavior of the expansion of $\mathfrak{S} _{1^n×w}·\mathfrak{S} _{1^n×u}$ into Schubert polynomials, as $n$ increases. We prove that this expansion stabilizes and thus we get a natural expansion for the product of two Stanley symmetric functions. In the case when one permutation is Grassmannian, we have a better understanding of this stability.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Stanley symmetric functions, Schubert polynomials, Littlewood-Richardson rule,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]