2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69321Motivated by Stanley's results in \cite{St02}, we generalize the rank of a partition $λ$ to the rank of a shifted partition $S(λ)$. We show that the number of bars required in a minimal bar tableau of $S(λ)$ is max$(o, e + (\ell(λ) \mathrm{mod} 2))$, where $o$ and $e$ are the number of odd and even rows of $λ$. As a consequence we show that the irreducible projective characters of $S_n$ vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur's $Q_λ$ symmetric functions in terms of the power sum symmetric functions.12 pages, 7 figuresCombinatorics05E05, 05E10, 20C25, 20C30text