Séminaire Lotharingien de Combinatoire, B38c (1996), 29 pp.

Rudolf Winkel

Recursive and Combinatorial Properties of Schubert Polynomials

Abstract. We describe two recursive methods for the calculation of Schubert polynomials and use them to give new relatively simple proofs of their basic properties. Moreover, we present (1) methods for the calculation of a reduced word for a permutation from its Lehmer code (and other small algorithms for the manipulation of Lehmer codes), (2) new determinantal formulas for certain Schubert polynomials, which `interpolate' the well known formulas for Schur polynomials, and (3) a fast and simple method for the recursive calculation of Schubert polynomials avoiding divided differences (thereby avoiding completely the computation of intermediary terms, which eventually cancel). The paper can be read as a short self contained introduction to Schubert polynomials providing full proofs.

Received: July 24, 1997; Accepted: December 3, 1997.

The following version is available: