2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226279This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of the hook lengths of p, are polynomial functions of n. A similar result is obtained for symmetric functions of the contents and shifted parts of n.20 pages. Correction of some inaccuracies, and a new Theorem 4.4Combinatorics05E05text