2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65705The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners.LaTeX, 26 pages, 44 figures, extended version of a talk given at the 14th International Conference on Formal Power Series and Algebraic Combinatorics (Melbourne 2002); Version2: Changed title, expanded some sections and included more picturesCombinatoricsMathematical PhysicsExactly Solvable and Integrable Systems05A15; 82B23text