Application of Inverse Kostka Matrix in the Study of Symmetric Functions

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9408221 Yang The main goal of this project is to investigate possible applications of the inverse Kostka matrix and its combinatorial interpretation in the study of symmetric functions. Problems to be considered include (1) expansion of plethysm of symmetric functions as a sum of Schur functions, (2) expansion of symmetric product as Schur function series, and (3) q-Schur function series and its properties. Since the expansion coefficients in these problems can be expressed in terms of the inverse Kostka matrix, it is expected that combinatorial properties of the matrix, in particular, knowing its zero elements, can greatly simplify the problems. ***