منابع مشابه
Avoidability of circular formulas
Clark has defined the notion of n-avoidance basis which contains the avoidable formulas with at most n variables that are closest to be unavoidable in some sense. The family Ci of circular formulas is such that C1 = AA, C2 = ABA.BAB, C3 = ABCA.BCAB.CABC and so on. For every i 6 n, the n-avoidance basis contains Ci. Clark showed that the avoidability index of every circular formula and of every ...
متن کاملAvoidability of Formulas with Two Variables
In combinatorics on words, a word w over an alphabet Σ is said to avoid a pattern p over an alphabet ∆ of variables if there is no factor f of w such that f = h(p) where h : ∆∗ → Σ∗ is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. We consider the patterns such that at most two variables appear at least twic...
متن کاملPattern Avoidability with Involution
An infinte word w avoids a pattern p with the involution θ if there is no substitution for the variables in p and no involution θ such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the size of the alphabet. For example, it is shown that the pattern α θ (α)α can be avoided over three letters but not two letters, whereas it is well known that α...
متن کاملOn some generalizations of abelian power avoidability
We prove that 2-abelian-cubes are avoidable over a binary alphabet and that 3-abelian-squares are avoidable over a ternary alphabet, answering positively to two questions of Karhumäki et al.. We also show the existence of infinite additive-cube-free words on several ternary alphabets. To achieve this, we give sufficient conditions for a morphism to be k-abelian-n-power-free (resp. additive-n-po...
متن کاملAvoidability of long k-abelian repetitions
We study the avoidability of long k-abelian-squares and k-abeliancubes on binary and ternary alphabets. For k = 1, these are Mäkelä’s questions. We show that one cannot avoid abelian-cubes of abelian period at least 2 in infinite binary words, and therefore answering negatively one question from Mäkelä. Then we show that one can avoid 3-abelian-squares of period at least 3 in infinite binary wo...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2018
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2017.11.014