2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73585The product $s_μs_ν$ of two Schur functions is one of the most famous examples of a Schur-positive function, i.e. a symmetric function which, when written as a linear combination of Schur functions, has all positive coefficients. We ask when expressions of the form $s_λs_ρ- s_μs_ν$ are Schur-positive. This general question seems to be a difficult one, but a conjecture of Fomin, Fulton, Li and Poon says that it is the case at least when $λ$ and $ρ$ are obtained from $μ$ and $ν$ by redistributing the parts of $μ$ and $ν$ in a specific, yet natural, way. We show that their conjecture is true in several significant cases. We also formulate a skew-shape extension of their conjecture, and prove several results which serve as evidence in favor of this extension. Finally, we take a more global view by studying two classes of partially ordered sets suggested by these questions.24 pages, 5 PostScript figures, multiple other figures use LaTeX picture environmentCombinatorics05E05 (Primary) 05E10 (Secondary)text