2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61424A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Groebner bases. Our main result is a bijection between virtual chambers of the configuration and virtual initial ideals of the associated binomial ideal.18 pages, 2 figuresCombinatoricsCommutative Algebra13P10, 52B20, 90C10text