Browsing James D. Currie by Title
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Squarefree Words with Squarefree Selfshuffles
(The Electronic Journal of Combinatorics, 20140112)We answer a question of Harju: For every n ≥ 3 there is a squarefree ternary word of length n with a squarefree selfshuffle. 
Suffix conjugates for a class of morphic subshifts
(Cambridge University Press, 201509)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 Squarefree Sequence Avoiding Factors Equivalent to abcacba
(The Electronic Journal of Combinatorics, 20160527)We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary squarefree words; we show that there is a ternary squarefree word avoiding letter pattern xyzxzyx. In fact, we characterize ... 
There are Ternary Circular SquareFree Words of Length n for n ≥ 18
(The Electronic Journal of Combinatorics, 20021011)There are circular squarefree 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
(The Electronic Journal of Combinatorics, 20040123)We show that there exist binary circular 5/2+ power free words of every length. 
Unary patterns under permutations
(Elsevier, 20180604)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, ... 
Words without NearRepetitions
(Canadian Mathematical Society, 19920601)We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of ...