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Binary Words Avoiding ***x* *x*^{R} *x* and Strongly Unimodal Sequences

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James Currie and Narad Rampersad

Department of Mathematics and Statistics

University of Winnipeg

515 Portage Avenue

Winnipeg, Manitoba R3B 2E9

Canada

**Abstract:**

In previous work, Currie and Rampersad showed that the growth of the
number of binary words avoiding the pattern
*x* *x* *x*^{R}
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* *x*^{R}.
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".

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(Concerned with sequences
A022567
A261204.)

Received August 12 2015; revised version received August 24 2015.
Published in *Journal of Integer Sequences*, September 14 2015.

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