Title: Multiplication of a Schubert polynomial by a Stanley symmetric polynomial,
Abstract: We prove, combinatorially, that the product of a Schubert polynomial by a
Stanley symmetric polynomial is a truncated Schubert polynomial. Using Monk's
rule, we derive a nonnegative combinatorial formula for the Schubert polynomial
expansion of a truncated Schubert polynomial. Combining these results, we give
a nonnegative combinatorial rule for the product of a Schubert and a Schur
polynomial in the Schubert basis.