2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73807Young tableaux are ubiquitous in various branches of mathematics. There are two counting formulas for standard Young tableaux. The first involves a determinant and goes back to Frobenius and Young, and the second is the hook formula by Frame, Robinson and Thrall. We present a generalization of the determinant formula for semistandard Young tableaux of given shape and of given content. Our counting formula -- though not a determinant -- is a generalization of the determinant formula by Frobenius and Young.12 pagesCombinatoricsRepresentation Theory05A15, 05A10 (Primary) 20C30 (Secondary)text