Browsing Department of Mathematics and Statistics by Title

Now showing items 21-37 of 37

    • 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 ...

    • Least Periods of Factors of Infinite Words 

      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 ...

    • Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics 

      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 ...

    • The metric dimension and metric independence of a graph 

      Currie, James; Oellerman, Ortrud R. (The Charles Babbage Research Centre, 2001)
      A vertex x of a graph G resolves two vertices u and v of G if the distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are ...

    • 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 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.

    • 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 ...

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

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

    • Regular Two-Graphs and Equiangular Lines 

      Gosselin, Shonda (University of WinnipegUniversity 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 ...

    • 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 ...

    • 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 ...

    • Skeleton Cave, Leigh Woods, Bristol 

      Mullan, G. J.; Meiklejohn, C.; Babb, J. (University of Bristol Spelaeological Society, 2017)
      An account is given of the discovery and excavation of this small cave in the 1960s. It is recorded that archaeological finds were made, but of these, only a single human mandible can now be traced. Radiocarbon dating shows ...

    • Sliding Down Inclines with Fixed Descent Time: a Converse to Galileo's Law of Chords 

      Babb, Jeff (Canadian Mathematical Society, 2008-12)

    • Square-free Words with Square-free Self-shuffles 

      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.

    • Supporting Teachers in Times of Change: The Job Demands- Resources Model and Teacher Burnout During the COVID-19 Pandemic 

      Sokal, Laura J.; Eblie Trudel, Lesley G.; Babb, Jeff C. (RedFame, 2020-10)
      Burnout in teachers has been broadly investigated, but no studies have investigated burnout in teachers during a pandemic. The current study is based on a survey of 1278 Canadian teachers and examined whether the Job ...

    • 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.

    • Unary patterns under permutations 

      Currie, James D.; Nowotka, Dirk; Manea, Florin; Reshadi, Kamellia (Elsevier, 2018-06-04)
      Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, ...