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Generalizing the Fundamental Theorem of Symmetric Polynomials
The fundamental theorem of symmetric polynomials tells us that the ring $\mathbb{Z}[x_1,\ldots,x_n]^{S_n}$ of symmetric polynomials in $n$ variables is generated (without relations) by the elementary ...
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Is there any simple formula for the character of $S_{n}$ represented by the set of $k$-tuples of $\{1,2,...,n\}$?
I'm interested in the representation theory of symmetric groups.
I'm now trying to search for the formula for the characters of $\Omega^{k}$, the set of $k$-tuple of elements of $\Omega$ a set of $n$ ...
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