  Based on Thomas and Yong's K-theoretic jeu de taquin algorithm, we prove a
uniform Littlewood-Richardson rule for the K-theoretic Schubert structure
constants of all minuscule homogeneous spaces. Our formula is new in all types.
For the main examples of Grassmannians of type A and maximal orthogonal
Grassmannians it has the advantage that the tableaux to be counted can be
recognized without reference to the jeu de taquin algorithm.
