Balanced labellings and Schubert polynomials

Abstract

We study Balanced labellings of diagrams representing the inversions in a permutation. These are known to be natural encodings of reduced decompositions of permutations w ∈ Σn, and we show that they also give combinatorial descriptions of both the Stanley symmetric functions Fw, and the Schubert polynomial G-fraktur signw associated with w. Furthermore, they lead to an explicit basis for the Schubert modules introduced by Kraskiewicz and Pragacz. © 1997 Academic Press Limited.