Slide polynomials and subword complexes

Abstract Subword complexes were defined by Knutson and Miller in 2004 to describe Gröbner degenerations of matrix Schubert varieties. a certain type are called pipe dream complexes. The facets such complex indexed dreams, or, equivalently, monomials the corresponding polynomial. In 2017 Assaf Searles basis slide polynomials, generalizing Stanley symmetric functions, described combinatorial rule for expanding polynomials this basis. We decomposition subword into strata appearing way shown be homeomorphic balls or spheres. For complexes, correspond polynomials. Bibliography: 14 titles.