Title: Fixed Q under the reverse operation in the RSK correspondence

 Abstract: The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate

where $w^r$ is the reverse permutation of $w$. We first give a broad counting problem and introduce notation. Next, we sketch the proof of the above identity.