1 8 Ju l 2 00 1 The Number of Tableaux which Contain a Given

For a (standard) Young tableau T on [k], say that a tableau T ′ on [n] contains T as a subtableau if the cells of T ′ containing the elements of [k] are arranged as in T . McKay, Morse, and Wilf recently introduced the idea of quasirandom permutations and used this to find the limiting probability (as n → ∞) that a tableau on [n] contains a given tableau on [k] as a subtableau. Stanley then used the theory of symmetric functions to obtain an exact formula for the number of tableaux on [n] which contain a given subtableau. Here we extend the quasirandom permutation approach to give another proof of Stanley’s formula, one which is independent of the theory of symmetric functions and group characters. Our method rests on an exact count of the n-involutions which contain a given k-permutation as a subsequence; we find that this number depends on the patterns of the initial sequences of the k-permutation.