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Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.

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Applying a simple involution to Hall-Littlewood polynomials

The transition matrix from the Schur functions to the HL symmetric functions is $K(t)$, the matrix of Kostka polynomials. This means that the transition matrix from $P(x;t)$ to $P(x;-t)$ is $K(t)^{-1} …
Scott Andrews's user avatar
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Counting a Modified Class of Standard Young Tableau

Assuming that I'm understanding your definition of an almost standard tableau, I have an observation. Note that if we take an almost standard tableau and rearrange the entries of column $\lambda_r+1$ …
Scott Andrews's user avatar