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A family of formulas with reversal of high avoidability index 

Currie, James; Mol, Lucas; Rampersad, Narad (World Scientific, 2017)
We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...
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Square-free Words with Square-free Self-shuffles 

Currie, James D.; Saari, Kalle (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.
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Extremal words in morphic subshifts 

Zamboni, Luca Q.; Saari, Kalle; Rampersad, Narad; Currie, James D. (Elsevier, 2014-01-22)
Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order \sigma on A, we call the smallest word with respect to \sigma starting with b in the shift orbit closure of x an extremal word of ...
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Avoidability index for binary patterns with reversal 

Currie, James D.; Lafrance, Phillip (2017)
For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.
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Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 

Blanchet-Sadri, F.; Currie, James D.; Rampersad, Narad; Fox, Nathan (Integers, 2014-02-20)
We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds ...
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Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101 

Currie, James D.; Johnson, Jesse T. (2020-05-19)
We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101.
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On avoidability of formulas with reversal 

Currie, James D.; Mol, Lucas; Rampersad, Narad (EDP Sciences, 2018-02-13)
While a characterization of unavoidable formulas (without reversal) is well-known, little is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas ...
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Unary patterns under permutations 

Currie, James D.; Nowotka, Dirk; Manea, Florin; Reshadi, Kamellia (Elsevier, 2018-06-04)
Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, ...
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Suffix conjugates for a class of morphic subshifts 

Currie, James D.; Rampersad, Narad; Saari, Kalle (Cambridge University Press, 2015-09)
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and ...
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Cubefree words with many squares 

Currie, James D.; Rampersad, Narad (Discrete Mathematics and Theoretical Computer Science, 2014-05-13)
We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n.
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AuthorCurrie, James D. (14)Rampersad, Narad (9)Currie, James (3)Saari, Kalle (3)Mol, Lucas (2)Nowotka, Dirk (2)Blanchet-Sadri, F. (1)Cassaigne, Julien (1)Crochemore, Maxime (1)Fox, Nathan (1)... View MoreSubjectSquares (2)automata (1)combinatorics on words (1)Combinatorics on words, avoidable patterns, patterns under permutations (1)combinatorics on words, circular words, necklaces, square-free words, non-repetitive sequences (1)combinatorics on words, pattern avoidance, patterns with reversal, avoidability index (1)combinatorics on words, words avoiding patterns, patterns with reversal (1)Cubefree words (1)Formula with reversal (1)Infinite words (1)... View MoreDate Issued
2010 - 2020 (17)
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