Abstract :
The shape of a Young diagram Y (|Y| = n) can be specified in terms of the set of symmetric power sums over its contents, σl = Σ(ij)ϵY(j − i)l; l = 1, 2, …, n. It is remarkable that the set of power sums σ1, σ2, …, σk is sufficient to characterize the Young diagrams possessing up to n(k) boxes, where n(k) is considerably larger than k. Numerical evidence for k⩽5 is roughly consistent with n(k) ∼ 4(43)2k. The lower bound n(k) > k + max(2, √k) has been derived by examination of some properties of Young diagrams with a large number of rows, and the upper bound n(k) < 22k+1 has been established using a variant of the Tarry-Escott problem.
