On the Lipschitz constant of the RSK correspondence

We view the RSK correspondence as associating to each permutation π ∈ S n a Young diagram λ = λ ( π ) , i.e. a partition of n. Suppose now that π is left-multiplied by t transpositions, what is the largest number of cells in λ that can change as a result? It is natural refer to this question as the search for the Lipschitz constant of the RSK correspondence. w upper bounds on this Lipschitz constant as a function of t. For t = 1 , we give a construction of permutations that achieve this bound exactly. For larger t we construct permutations which come close to matching the upper bound that we prove.