2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57018By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK correspondence. We also investigate birational Weyl group actions related to those algorithms.63 pages (Revised Version: Introduction is modified. Misprints are also corrected.)Mathematical PhysicsCombinatoricstext