Department of Mathematics and Statistics
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Opportunity solving: Ordinary people doing extraordinary things, every day
(Canadian Education Network, 2020-10-16) -
Canadian teachers' attitudes toward change, efficacy, and burnout during the COVID-19 pandemic
(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
(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
(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 ... -
Supporting Teachers in Times of Change: The Job Demands- Resources Model and Teacher Burnout During the COVID-19 Pandemic
(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 ... -
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
(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 ... -
A family of formulas with reversal of high avoidability index
(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 metric dimension and metric independence of a graph
(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 ... -
The number of order–preserving maps of fences and crowns
(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. -
Counting endomorphisms of crown-like orders
(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. -
The Complexity of the Simplex Algorithm
(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
(Cambridge University Press, 1982) -
Shuffling and unshuffling
(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
(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
(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 ... -
Square-free Words with Square-free Self-shuffles
(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. -
Cyclically t-complementary uniform hypergraphs
(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 t1 partition the set of all ... -
Self-Complementary Hypergraphs
(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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