2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212328We show a new lower bound for the maximum number of runs in a string. We prove that for any e > 0, (a -- e)n is an asymptotic lower bound, where a = 56733/60064 = 0.944542. It is superior to the previous bound 0.927 given by Franek et al. Moreover, our construction of the strings and the proof is much simpler than theirs.Discrete MathematicsG.2.1text