2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202867We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead to general N-soliton solutions of the box-ball system.52 pagesQuantum AlgebraMathematical PhysicsExactly Solvable and Integrable Systemstext