2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144583We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical reflection argument. A refinement allows for the counting of paths with a specified number of corners. We also apply the result to examine paths dominated by periodic boundaries.20 pages, 13 figuresCombinatorics05A15text