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arXiv · 1508.02964

Binary words avoiding xx^Rx and strongly unimodal sequences

James D. Currie·Narad Rampersad
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Abstract

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxx^R 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 xx^Rx. Curiously, the analysis for xx^Rx is much simpler than that for xxx^R. We derive our results by giving a bijection between the set of binary words avoiding xx^Rx and a class of sequences closely related to the class of "strongly unimodal sequences."

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James D. Currie, Narad Rampersad. 2015-08-12. Binary words avoiding xx^Rx and strongly unimodal sequences. https://arxiv.org/abs/1508.02964

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