  Schubert polynomials form a basis of the polynomial ring. This basis and its
structure constants have received extensive study. Recently, Pan and Yu
initiated the study of top Lascoux polynomials. These polynomials form a basis
of a subalgebra of the polynomial ring where each graded piece has finite
dimension. This paper connects Schubert polynomials and top Lascoux polynomials
via a simple operator. We use this connection to show these two bases share the
same structure constants. We also translate several results on Schubert
polynomials to top Lascoux polynomials, including combinatorial formulas for
their monomial expansions and supports.
