# Rings with bases and Schubert polynomials

A category central to algebraic combinatorics is that of “rings with bases”. We’ll look at a very simple example, the nil Hecke algebra, and its action on polynomials in infinitely many variables. The resulting dual basis is the “Schubert polynomials”. Surprisingly, these have positive coefficients, which we will compute by counting “pipe dreams”.

**Date published:**Wednesday, January 11, 2023