Binary Words Avoiding x xR x and Strongly Unimodal Sequences
James Currie and Narad Rampersad
Department of Mathematics and Statistics
University of Winnipeg
515 Portage Avenue
Winnipeg, Manitoba R3B 2E9
In previous work, Currie and Rampersad showed that the growth of the
number of binary words avoiding the pattern
x x xR
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 xR x .
Curiously, the analysis for
x xR x
is much simpler than that for
x x xR.
We derive our results by giving a bijection between the set of
binary words avoiding
x xR x
and a class of sequences closely related to
the class of "strongly unimodal sequences".
Full version: pdf,
(Concerned with sequences
Received August 12 2015; revised version received August 24 2015.
Published in Journal of Integer Sequences, September 14 2015.
Journal of Integer Sequences home page