A canonical expansion of the product of two Stanley symmetric functions

作者：Li Nan^*

来源：Journal of Algebraic Combinatorics, 2014, 39(4): 833-851.

DOI：10.1007/s10801-013-0469-2

• Schubert polynomials
• Stanley symmetric functions
• Maximal transition tree

We study the problem of expanding the product of two Stanley symmetric functions F (w) a <...F (u) into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial , and study the behavior of the expansion of 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. We then study some other related stability properties, providing a second proof of the main result.

• 出版日期2014-6
• 单位MIT