Now showing items 31-40 of 40

    • The number of order–preserving maps of fences and crowns 

      Currie, James; Visentin, Terry I. (Springer, 1991-06)
      We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results.
    • The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially 

      Currie, James; Rampersad, Narad; Aberkane, Ali (2004-06-19)
      We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^{1/24}
    • 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 ...
    • 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, ...
    • Words without Near-Repetitions 

      Currie, J.; Bendor-Samuel, A. (Canadian Mathematical Society, 1992-06-01)
      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 ...