Department of Mathematics and Statistics

Recent Submissions

  • Opportunity solving: Ordinary people doing extraordinary things, every day 

    Sokal, Laura; Eblie Trudel, Lesley; Babb, Jeff (Canadian Education Network, 2020-10-16)

  • 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.

  • 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 ...

  • 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 ...

  • 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 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 ...

  • Class Numbers and Biquadratic Reciprocity 

    Williams, Kenneth S.; Currie, James D. (Cambridge University Press, 1982)

  • Shuffling and unshuffling 

    Henshall, Dane; Rampersad, Narad; Shallit, Jeffrey (Bulletin of the European Association for Theoretical Computer Science, 2012)
    We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal ...

  • 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.

  • 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 ...

  • 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 ...

  • Self-Complementary Hypergraphs 

    Gosselin, Shonda (University of OttawaUniversity of Ottawa and Carleton University (joint program), 2009)
    In this thesis, we survey the current research into self-complementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which ...

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