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Now showing items 11-17 of 17
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
(2015-09-14)
In previous work, Currie and Rampersad showed that the growth of the number
of binary words avoiding the pattern xxxR was intermediate between polynomial and
exponential. We now show that the same result holds for the ...
Square-free Words with Square-free Self-shuffles
(The Electronic Journal of Combinatorics, 2014-01-12)
We answer a question of Harju: For every n ≥ 3 there is a square-free ternary word of length n with a square-free self-shuffle.
Growth rate of binary words avoiding xxxR
(Elsevier, 2016-01)
Abstract
Consider the set of those binary words with no non-empty factors of the form
xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows
polynomially or exponentially with length. In this ...
Infinite words containing squares at every position
(EDP Sciences, 2010)
Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...
Avoiding three consecutive blocks of the same size and same sum
(Association of Computing Machinery, 2014-04)
We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994.
Avoidability index for binary patterns with reversal
(The Electronic Journal of Combinatorics, 2016-02-19)
For every pattern p over the alphabet {x, x^R, y, y^R}, we specify the least k such that p is k-avoidable.
A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba
(The Electronic Journal of Combinatorics, 2016-05-27)
We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we characterize ...