Binary words avoiding xxʳx and strongly unimodal sequences

الأصل · EN

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxxʳ was intermediate between polynomial and exponential. We now show that the same holds for the growth of the number of binary words avoiding the pattern xxʳx. Curiously, the analysis for xxʳx is much simpler than that for xxxʳ. We derive our results by giving a bijection between the set of binary words avoiding xxʳx and a class of sequences closely related to the class of "strongly unimodal sequences."