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added pointer to Sagan’s textbook and encyclopedia article, and pointer to where in there the Frobenius formula
$s_\lambda \;=\; \frac{1}{n!} \underset {\sigma \in Sym(n)} {\sum} \chi^{(\lambda)}(\sigma) \cdot p_\sigma$is discussed.
(I did not find it mentioned in either of Macdonald’s, James’s or Diaconis’ textbook)
Well done! I’d only seen it in Qiaochu Yuan’s post.
Yes, thanks, I had followed your links here, where the statement is recorded (out of the blue) as Def. 2 there.
The only reference given in that post is to
but I don’t see the formula in there either. In his other post he cites Sagan, though, and so possibly that’s again the source from which he got that formula.
added (here) the equivalent description in terms of sums over semistandard Young tableaux.
(Wrote this as a proposition under “Properties”, but c iting Sagan01, who gives this as the definition. Need to give a reference for the proof of the equivalence to the original Jacobi-style definition.)
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