Browsing Department of Mathematics and Statistics by Author "Currie, James"
Now showing items 1-10 of 10
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Avoidability index for binary patterns with reversal
(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. -
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 ... -
A Characterization of Fractionally Well-Covered Graphs
(Ars Combinatoria, 1991)A graph is called well-covered if every maximal independent set has the same size. One generalization of independent sets in graphs is that of a fractional cover -- attach nonnegative weights to the vertices and require ... -
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 ... -
Dejean's conjecture holds for n ≥ 27
(EDP Sciences, 2009)We show that Dejean’s conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible. -
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 ... -
Infinite words containing squares at every position
(EDP Sciences, 2010)Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ... -
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. -
The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially
(2004-06-19)We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^{1/24}
