##### Department of Mathematics,

University of California San Diego

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### Combinatorics Seminar (Math 269)

## Tianyi Yu

#### UCSD

## Top degree components of Grothendieck and Lascoux Polynomials

##### Abstract:

The Schubert polynomials and key polynomials form two important bases for the polynomial ring. Schubert and key polynomials are the``bottom layers” of Grothendieck and Lascoux polynomials, two inhomogeneous polynomials. In this talk, we look at their``top layers”. We develop a diagrammatic way to compute the degrees and the leading monomials of these top layers. Finally, we describe the Hilbert series of the space spanned by these top layers, involving a classical $q$-analogue of the Bell numbers.

### January 24, 2023

### 4:00 PM

APM 7321

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