2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60184A survey of recent progress in three areas of algebraic combinatorics: (1) the Saturation Conjecture for Littlewood-Richardson coefficients, (2) the n! and (n+1)^{n-1} conjectures, and (3) longest increasing subsequences of permutations.22 pages, submitted to the proceedings of Mathematical Challenges for the 21st Century, UCLA, August 7-12, 2000; revision updates references and adds slightly more material on the Hilbert scheme of points in the planeCombinatorics05Exxtext