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Department of Mathematics and Statistics

Department of Mathematics and Statistics

 

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  • Currie, James D. (The Electronic Journal of Combinatorics, 1995-10-14)
    We can compress the word 'banana' as xyyz, where x= 'b', y= 'an',z= 'a'. We say that 'banana' encounters yy. Thus a 'coded' version of yy shows up in 'banana'. The relation 'u encounters w' is transitive, and thus generates ...
  • 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. (The Electronic Journal of Combinatorics, 2002-07-03)
    In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...
  • 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.
  • 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.
  • 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.
  • 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 ...
  • 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 ...
  • 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.
  • 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.
  • Babb, J. C.; Dempster, C. J.; Wallis, R. J. (NRC Research Press, 1989-01)
    A statistical regression model for rapid prediction of moisture content based on measurements of dielectric capacitance and test weight was developed for Eastern Canadian corn (Zea mays L.). For 336 samples of the 1986 ...
  • Babb, Jeff (2005)
    This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323–1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Gosselin, Shonda (Discrete Mathematics, 2009-09)
    For an integer n and a prime p, let n.p/ D maxfi V pi divides ng. In this paper, we present a construction for vertex-transitive self-complementary k-uniform hypergraphs of order n for each integer n such that pn.p/ 1 ...
  • 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 ...
  • 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 ...
  • Gosselin, Shonda (University of Ottawa, 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 ...
  • Gosselin, Shonda (University of Waterloo, 2004)
    Regular two-graphs are antipodal distance-regular double coverings of the complete graph, and they have many interesting combinatorial properties. We derive a construction for regular two-graphs containing cliques of ...