Browsing by Author "Currie, James"
Now showing items 110 of 10

Avoidability index for binary patterns with reversal
Currie, James; Lafrance, Philip (The Electronic Journal of Combinatorics, 20160219)For every pattern p over the alphabet {x, x^R, y, y^R}, we specify the least k such that p is kavoidable. 
The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem
Babb, Jeff; Currie, James (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 WellCovered Graphs
Currie, James; Nowakowski, Richard (Ars Combinatoria, 1991)A graph is called wellcovered 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
Currie, James (Carleton UniversityCarleton University, 198408)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 KleeMinty. Because of the bad behaviour ... 
Dejean's conjecture holds for n ≥ 27
Currie, James; Rampersad, Narad (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
Currie, James; Mol, Lucas; Rampersad, Narad (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
Currie, James; Rampersad, Narad (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 αpowers but contains arbitrarily large squares beginning at every position? We resolve ... 
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 ... 
The number of order–preserving maps of fences and crowns
Currie, James; Visentin, Terry I. (Springer, 199106)We perform an exact enumeration of the orderpreserving maps of fences (zigzags) and crowns (cycles). From this we derive asymptotic results. 
The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially
Currie, James; Rampersad, Narad; Aberkane, Ali (20040619)We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^{1/24}