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A combinatorial interpretation of the inverse Kostka matrix. (English) Zbl 0735.05013
The authors provide a combinatorial interpretation of \(K^{-1}\) where \(K\) is the Kostra matrix by using Jacobi-Trudi identity. This interpretation is then used to show combinatorially that \(KK^{-1}=I\). Furthermore, a combinatorial proof of the generalized Jacobi-Trudi identity is given via rim hook tabloids. An application of the results in the paper is also given.
Reviewer: D.V.Chopra

05A99 Enumerative combinatorics
05E05 Symmetric functions and generalizations
Full Text: DOI
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