Asymptotic number of isometric generalized Fibonacci cubes

AbstractFor a binary word f, let Qd(f) be the subgraph of the d-dimensional cube Qd induced on the set of all words that do not contain f as a factor. Let Gn be the set of words f of length n that are good in the sense that Qd(f) is isometric in Qd for all d. It is proved that limn→∞|Gn|/2n exists. Estimates show that the limit is close to 0.08, that is, about eight percent of all words are good