2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170271In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference s_A - s_B of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Our conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for s_A = s_B, and we deduce a strengthening of their result as a special case.12 pages, 4 figures. Fixed typos; final version. To appear in the Journal of Algebraic CombinatoricsCombinatorics05E05 (Primary); 05E10, 06A07, 20C30 (Secondary)text