2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156093We give an explicit Grobner basis for the ideal of the tangent cone at any T-fixed point of a Richardson variety in the Grassmannian, thus generalizing a result of Kodiyalam-Raghavan and Kreiman-Lakshmibai. Our proof is based on a generalization of the Robinson-Schensted-Knuth (RSK) correspondence, which we call the bounded RSK (BRSK). We use the Grobner basis result to deduce a formula which computes the multiplicity of the Richardson variety at any T-fixed point by counting families of nonintersecting lattice paths, thus generalizing a result first proved by Krattehthaler.34 pages, final version, many revisions, to appear in Journal of Algebraic CombinatoricsAlgebraic GeometryCommutative AlgebraCombinatorics14M15; 05E10text