2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67012It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 7/3. More precisely, there are only polynomially many binary words of length n that avoid 7/3-powers, but there are exponentially many binary words of length n that avoid (7/3+)-powers. This answers an open question of Kobayashi from 1986.12 pagesCombinatoricsDiscrete Mathematics68R15text