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Browsing Department of Mathematics and Statistics by Title

Browsing Department of Mathematics and Statistics by Title

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  • 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 ...
  • 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 ...
  • Meiklejohn, Christopher; Schulting, Rick; Musgrave, Jonathan; Babb, Jeff; Higham, Thomas; Richards, David; Mullan, Graham (University of Bristol Spelaeological Society, 2012)
    Aveline's Hole is both one of the best-known sites with early human skeletal material in Britain and one of the most problematic in its history. First discovered and explored at the close of the 18th century, it yielded ...
  • Currie, James; Lafrance, Philip (The Electronic Journal of Combinatorics, 2016-02-19)
    For every pattern p over the alphabet {x, x^R, y, y^R}, we specify the least k such that p is k-avoidable.
  • 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. ...
  • 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.
  • Meiklejohn, Christopher; Babb, Jeff; Hiebert, Weldon (Landesamt für Denkmalpflege und Archäologie Sachsen-Anhalt, 2016)
    Over the past decade we have focused on two interrelated topics within Mesolithic burial studies, the relationship between burial number and burial date, and the chronology of Mesolithic sites with burials. Related to this ...
  • Crochemore, Maxime; Currie, James D.; Kucherov, Gregory; Nowotka, Dirk (Dagstuhl Publishing, 2014-03-09)
    Strings (aka sequences or words) form the most basic and natural data structure. They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words ...
  • Gosselin, Shonda (Journal of Combinatorial Designs, 2011-02-17)
    In this paper, we examine the possible orders of t-subset-regular selfcomplementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and Tayfeh- Rezaie's ...
  • 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.
  • 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 ...
  • Gosselin, Shonda (European Journal of Combinatorics, 2010-05)
    A cyclically t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation 2 Sym.V/ such that the sets E; E ; E 2; : : : ; E t􀀀1 partition the set of all ...
  • 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.
  • Allouche, Jean-Paul; Currie, James D.; Shallit, Jeffrey (The Electronic Journal of Combinatorics, 1998-05-03)
    Let t be the infinite fixed point, starting with 1, of the morphism μ:0→01, 1→10. An infinite word over {0,1} is said to be overlap-free if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ...
  • 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 ...
  • 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 ...
  • Gosselin, Shonda (Discrete Mathematics, 2010-02)
    In 2007, Szymanski and Wojda proved that for positive integers n; k with k<n, a self-complementary k-uniform hypergraph of order n exists if and only if n/k is even. In this paper, we characterize the cycle type of a ...
  • 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 ...
  • Currie, James D.; Saari, Kalle (EDP Sciences, 2009)
    We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ...

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