Séminaire Lotharingien de Combinatoire, B38c (1996), 29
Recursive and Combinatorial Properties of Schubert Polynomials
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: