Now showing items 1-20 of 25

    • Abelian complexity of fixed point of morphism 0 -> 012, 1 -> 02, 2 -> 1 

      Currie, James D.; Blanchet-Sadri, Francine; Fox, Nathan; Rampersad, Narad (2016-02-14)
      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 ...
    • 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 ...
    • Automaticity of Primitive Words and Irreducible Polynomials 

      Lacroix, Anne; Rampersad, Narad (Discrete Mathematics and Theoretical Computer Science, 2013)
      If L is a language, the automaticity function AL(n) (resp. NL(n)) of L counts the number of states of a smallest deterministic (resp. non-deterministic) finite automaton that accepts a language that agrees with L on all ...
    • Avoiding approximate repetitions with respect to the longest common subsequence distance 

      Camungol, Serina; Rampersad, Narad (Mathematical Sciences Publishers, 2015-09-17)
      Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form x x', where x and x' are close to being identical. ...
    • Binary Words Avoiding xxRx and Strongly Unimodal Sequences 

      Currie, James D.; Rampersad, Narad (2015-09-14)
      In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxxR was intermediate between polynomial and exponential. We now show that the same result holds for the ...
    • Binary Words Containing Infinitely Many Overlaps 

      Currie, James D.; Rampersad, Narad; Shallit, Jeffrey (The Electronic Journal of Combinatorics, 2006-09-22)
      We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps.
    • 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.
    • Cyclic Complexity of Some Infinite Words and Generalizations 

      Krawchuk, Colin; Rampersad, Narad (Integers, 2018-03)
      Cassaigne et al. introduced the cyclic complexity function c_x(n), which gives the number of cyclic conjugacy classes of length-n factors of a word x. We study the behavior of this function for the Fibonacci word f and the ...
    • Dejean's conjecture holds for n ≥ 27 

      Currie, James; Rampersad, Narad (EDP Sciences, 2009)
      We show that Dejean’s conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.
    • 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 ...
    • 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 ...
    • For each a > 2 there is an Infinite Binary Word with Critical Exponent a 

      Currie, James D.; Rampersad, Narad (The Electronic Journal of Combinatorics, 2008-08-31)
      The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ...
    • Further applications of a power series method for pattern avoidance 

      Rampersad, Narad (The Electronic Journal of Combinatorics, 2011-06-21)
      In combinatorics on words, a word w over an alphabet ∑ is said to avoid a pattern p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ...
    • Growth rate of binary words avoiding xxxR 

      Currie, James D.; Rampersad, Narad (Elsevier, 2016-01)
      Abstract Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this ...
    • Infinite words containing squares at every position 

      Currie, James; Rampersad, Narad (EDP Sciences, 2010)
      Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...
    • The minimal automaton recognizing mN in a linear numeration system 

      Charlier, Émilie; Rampersad, Narad; Rigo, Michel; Waxweiler, Laurent (Integers, 2011-12-02)
      We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component ...
    • Multi-dimensional sets recognizable in all abstract numeration systems 

      Charlier, Émilie; Lacroix, Anne; Rampersad, Narad (EDP Sciences, 2011)
      We prove that the subsets of Nd that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
    • 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 ...