Now showing items 1-20 of 29

    • 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 ...
    • Attainable lengths for circular binary words avoiding k-powers 

      Currie, James D.; Aberkane, Ali (The Belgian Mathematical Society, 2005)
      We show that binary circular words of length n avoiding 7/3+ powers exist for every sufficiently large n. This is not the case for binary circular words avoiding k+ powers with k < 7/3
    • The Aveline's Hole 9 Cranium: A Partial Solution to a Long Standing Enigma 

      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 ...
    • Avoidability index for binary patterns with reversal 

      Currie, James D.; Lafrance, Phillip (2017)
      For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.
    • 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. ...
    • Avoiding Patterns in the Abelian Sense 

      Currie, J.; Linek, V. (Canadian Mathematical Society, 2001-08)
      We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some ...
    • 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 ...
    • The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem 

      Babb, Jeff; Currie, James (Montana Council of Teachers of Mathematics & Information Age Publishing, 2008)
      Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of ...
    • Canadian teachers' attitudes toward change, efficacy, and burnout during the COVID-19 pandemic 

      Sokal, Laura; Eblie Trudel, Lesley; Babb, Jeff (Elsevier, 2020-11-19)
      Canadian teachers (N = 1626) took part in a longitudinal, national survey conducted at two points early in the COVID-19 pandemic. Results indicated that teacher efficacy, attitudes toward change, and perceptions of ...
    • Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101 

      Currie, James D.; Johnson, Jesse T. (2020-05-19)
      We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101.
    • Class Numbers and Biquadratic Reciprocity 

      Williams, Kenneth S.; Currie, James D. (Cambridge University Press, 1982)
    • The Complexity of the Simplex Algorithm 

      Currie, James (Carleton UniversityCarleton University, 1984-08)
      The thesis begins by giving background in linear programming and Simplex methods. Topics covered include the duality theorem, Lemke's algorithm, and the pathological programs of Klee-Minty. Because of the bad behaviour ...
    • Counting endomorphisms of crown-like orders 

      Currie, James D.; Visentin, Terry I. (Springer, 2002-12)
      The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type.
    • COVID-19’s Second Wave: How are teachers faring with the return to physical schools? 

      EdCan. Well at Work; Ranby, Sarah; Rebeiz, André; Sokal, Laura; Eblie Trudel, Lesley; Babb, Jeff (Canadian Education Network, 2020-11-20)
    • Cyclically t-complementary uniform hypergraphs 

      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 ...
    • 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.
    • A direct proof of a result of Thue 

      Currie, James D. (Utilitas Mathematica, 1984)
    • 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 ...