  We obtain an identity between Fredholm determinants of two kinds of
operators, one acting on functions on the unit circle and the other acting on
functions on a subset of the integers. This identity is a generalization of an
identity between a Toeplitz determinant and a Fredholm determinant that has
appeared in the random permutation context. Using this identity, we prove, in
particular, convergence of moments for arbitrary rows of a random Young diagram
under Plancherel measure.
