2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66822The ring of locally-constant integer-valued functions on the dominant chamber of the Shi arrangement is endowed with a filtration and a new basis, compatible with this filtration, is found. This basis is compared to the trivial basis. The ring is given a presentation by generators and relations.7 pages, 2 figuresCombinatorics06A11;52C35text