347,479 research outputs found
Binary Patterns in Binary Cube-Free Words: Avoidability and Growth
The avoidability of binary patterns by binary cube-free words is investigated
and the exact bound between unavoidable and avoidable patterns is found. All
avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the
growth rates of the avoiding languages are studied. All such languages, except
for the overlap-free language, are proved to have exponential growth. The exact
growth rates of languages avoiding minimal avoidable patterns are approximated
through computer-assisted upper bounds. Finally, a new example of a
pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons
Days 2012
Computing the Partial Word Avoidability Indices of Binary Patterns
We complete the classification of binary patterns in partial words that was started in earlier publications by proving that the partial word avoidability index of the binary pattern ABABA is two and the one of the binary pattern ABBA is three
Binary patterns in the Prouhet-Thue-Morse sequence
We show that, with the exception of the words and , all
(finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can
actually be found in that sequence as segments (up to exchange of letters in
the infinite case). This result was previously attributed to unpublished work
by D. Guaiana and may also be derived from publications of A. Shur only
available in Russian. We also identify the (finitely many) finite binary
patterns that appear non trivially, in the sense that they are obtained by
applying an endomorphism that does not map the set of all segments of the
sequence into itself
Binary patterns in binary cube-free words: Avoidability and growth
The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given. © 2014 EDP Sciences
On the aperiodic avoidability of binary patterns with variables and reversals
In this work we present a characterisation of the avoidability of all unary and binary patterns, that do not only contain variables but also reversals of their instances, with respect to aperiodic infinite words. These types of patterns were studied recently in either more general or particular cases
Computing the Partial Word Avoidability Indices of Ternary Patterns
We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns' avoidability indices or at least give bounds for them
Avoidability of formulas with two variables
In combinatorics on words, a word over an alphabet is said to
avoid a pattern over an alphabet of variables if there is no
factor of such that where is a
non-erasing morphism. A pattern is said to be -avoidable if there exists
an infinite word over a -letter alphabet that avoids . We consider the
patterns such that at most two variables appear at least twice, or
equivalently, the formulas with at most two variables. For each such formula,
we determine whether it is -avoidable, and if it is -avoidable, we
determine whether it is avoided by exponentially many binary words
A generating function for bit strings with no Grand Dyck pattern matching
Abstract
We study the construction and the enumeration of bit strings, or binary words in {0, 1}*, having more 1's than 0's and avoiding a set of Grand Dyck patterns which form a cross-bifix-free set. We give a particular jumping and marked succession rule which describes the growth of such words according to the number of 1's. Then, we give the enumeration of the class by means of generating function
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