681 research outputs found
Growth rate of binary words avoiding
Consider the set of those binary words with no non-empty factors of the form
. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words
grows polynomially or exponentially with length. In this paper, we demonstrate
the existence of upper and lower bounds on the number of such words of length
, where each of these bounds is asymptotically equivalent to a (different)
function of the form , where , are constants
Binary words avoiding xx^Rx and strongly unimodal sequences
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."Comment: 4 page
Attainable lengths for circular binary words avoiding k-powers
We show that binary circular words of length n avoiding 7/3+ powers exist
for every sufficiently large n. This is not the case for binary circular words
avoiding k+ powers with k < 7/3https://projecteuclid.org/download/pdf_1/euclid.bbms/113379334
Avoidability index for binary patterns with reversal
For every pattern over the alphabet , we specify the
least such that is -avoidable.Comment: 15 pages, 1 figur
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