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Presented By: Learning Seminar in Algebraic Combinatorics - Department of Mathematics

Two Bases of the Polynomial Ring: Schubert Polynomials and Key Polynomials

Tianyi Yu

The polynomial ring has two distinct bases: Schubert polynomials and key polynomials. In this talk, we will first study the vector subspace spanned by Schubert polynomials in S_n, and describe another basis consisting of key polynomials. Then we will explore the process of expanding a Schubert polynomial into a sum of key polynomials, demonstrating how these two bases are interrelated.

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