On the inverse Kostka matrix

In the ring of symmetric functions the inverse Kostka matrix appears as the transition matrix from the bases given by monomial symmetric functions to the Schur bases. We present both a combinatorial characterization and a recurrent formula for the entries of the inverse Kostka matrix which are different from the results obtained by Egecioglu and Remmel (Linear Multilinear Algebra 26 (1990) 59). An application to the topology of the classifying space BU(n) is obtained. (C) 2003 Elsevier Inc. All rights reserved.