Department of Mathematics and Statistics
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Soumissions récentes
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COVID-19’s Second Wave: How are teachers faring with the return to physical schools?
(Canadian Education Network, 2020-11-20) -
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 ... -
Extremal words in morphic subshifts
(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 ... -
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 ... -
Avoidability index for binary patterns with reversal
(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. -
Attainable lengths for circular binary words avoiding k-powers
(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 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 Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem
(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 ... -
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. -
Avoiding Patterns in the Abelian Sense
(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 ... -
A direct proof of a result of Thue
(Utilitas Mathematica, 1984) -
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 ...