2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115497A graceful n-permutation is a graceful labeling of an n-vertex path P_n. In this paper we improve the asymptotic lower bound on the number of such permutations from (5/3)^n to 2.37^n. This is a computer-assisted proof based on an effective algorithm that enumerates graceful n-permutations. Our algorithm is also presented in detail.5 pages, 1 figureCombinatorics05C78 (Primary), 11Y55 (Secondary)text