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Let $\lambda,\mu,\nu$ be some partitions. Let's denote with $s_\lambda,s_\mu,s_\nu$ the Schur functions associated to these partitions. If

$s_\mu s_\nu=\sum_\lambda c^\lambda_{\mu\nu}s_\lambda$

then the Schur skew function is

$s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu\nu}s_\nu$

how can I prove that $s_{\lambda/\mu}=\sum_T x^T$ where $T$ is a tableaux of shape $\lambda/\mu$? (so we are supposing that $\mu\subset\lambda$)

(I know that $c^\lambda_{\mu\nu}=0$ if $|\lambda|\neq |\mu|+|\nu|$)

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    @draks: That depends on how your symmetric functions are given. On many pairs of bases a combinatorial expression is known for the scalar product between their elements, although this does not mean the value is easily calculated.2012-03-31

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