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Edit: This doesn't answer the question; see comments. Knuth, TAoCP3, p. 76, exercise 5 in section 5.1.4: Let $P$ be the tableau corresponding to the permutation $a_1a_2...a_n$; use exercise 4 to prove that $P^T$ is the tableau corresponding to $a_n...a_2a_1$. |
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You may be interested in Theorem 4.1.1, formula (12) of
Marc A. A. van Leeuwen Knuth, The Robinson-Schensted and SchÄutzenberger algorithmsTAoCP3, an elementary approachp. EDIT76, exercise 5 in section 5.1.4:confused Schützenberger with transpose. Let $P$ be the tableau corresponding to the permutation $a_1a_2...a_n$; use exercise 4 to prove that $P^T$ is the tableau corresponding to $a_n...a_2a_1$. |
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