Geodesic
Binary words avoiding \(xx^Rx\) and strongly unimodal sequences
Journal of integer sequences, Tome 18 (2015) no. 10
In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern $x x^{R} x$ was intermediate between polynomial and exponential. We now show that the same result holds for the growth of the number of binary words avoiding the pattern $x x^{R} x$ . Curiously, the analysis for $x x^{R} x$ is much simpler than that for $x x^{R} x$ . We derive our results by giving a bijection between the set of binary words avoiding $x x^{R} x$ and a class of sequences closely related to the class of "strongly unimodal sequences".
Classification : 68R15
Keywords: pattern with reversal, avoidability in words, strongly unimodal sequence 
@article{JIS_2015__18_10_a0,
     author = {Currie,  James and Rampersad,  Narad},
     title = {Binary words avoiding {\(xx^Rx\)} and strongly unimodal sequences},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1329.68194},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a0/}
}
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%A Rampersad,  Narad
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Currie,  James; Rampersad,  Narad. Binary words avoiding \(xx^Rx\) and strongly unimodal sequences. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a0/