Browsing Department of Mathematics and Statistics by Author "Currie, James D."
Now showing items 21-26 of 26
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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. -
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 ... -
A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba
Currie, James D. (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 ... -
There are Ternary Circular Square-Free Words of Length n for n ≥ 18
Currie, James D. (The Electronic Journal of Combinatorics, 2002-10-11)There are circular square-free words of length n on three symbols for n≥18. This proves a conjecture of R. J. Simpson. -
There Exist Binary Circular 5/2+ Power Free Words of Every Length
Aberkane, Ali; Currie, James D. (The Electronic Journal of Combinatorics, 2004-01-23)We show that there exist binary circular 5/2+ power free words of every length. -
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, ...