A combinatorial interpretation of the inverse kostka matrix |
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Authors: |
mer E¯ ecio¯ lu Jeffrey B Remmel |
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Institution: |
a Department of Computer Science, University of California, Santa Barbara, California
b Department of Mathematics, University of California-San Diego, La Jolla, California, California |
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Abstract: | The Kostka matrix K relates the. homogeneous and the Schur bases in the ring of symmetric functions where Kλ,μenumerates the number of column strict tableaux of shape λ and type μ. We make use of the Jacobi -Trudi identity to give a combinatorial interpretation for the inverse of the Kostka matrix in terms of certain types of signed rim hook tabloids. Using this interpretation, the matrix identity KK-1=Iis given a purely combinatorial proof. The generalized Jacobi-Trudi identity itself is also shown to admit a combinatorial proof via these rim hook tabloids. A further application of our combinatorial interpretation is a simple rule for the evaluation of a specialization of skew Schur functions that arises in the computation of plethysms. |
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Keywords: | |
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