2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118068The purpose of this short communication is to make some observations on the connections between various existing formulas of counting the number of sublattices of a fixed index in an $n$-dimensional lattice and their connection with the Gaussian binomials.AMS-Latex, preprint 3 pagesCombinatoricsNumber Theorytext