Browsing James D. Currie by Issue Date
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Class Numbers and Biquadratic Reciprocity
(Cambridge University Press, 1982) 
A direct proof of a result of Thue
(Utilitas Mathematica, 1984) 
The Complexity of the Simplex Algorithm
(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 ... 
Non repetitive walks in graphs and digraphs
(The University of CalgaryUniversity of Calgary, 198706)A word $w$ over alphabet $\Sigma$ is {\em nonrepetitive} if we cannot write $w=abbc$, $a,b,c\in\Sigma^*$, $b\ne\epsilon$. That is, no subword of $w$ appears twice in a row in $w$. In 1906, Axel Thue, the Norwegian number ... 
A Characterization of Fractionally WellCovered Graphs
(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 number of order–preserving maps of fences and crowns
(Springer, 199106)We perform an exact enumeration of the orderpreserving maps of fences (zigzags) and crowns (cycles). From this we derive asymptotic results. 
Words without NearRepetitions
(Canadian Mathematical Society, 19920601)We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of ... 
A Note on Antichains of Words
(The Electronic Journal of Combinatorics, 19951014)We can compress the word 'banana' as xyyz, where x= 'b', y= 'an',z= 'a'. We say that 'banana' encounters yy. Thus a 'coded' version of yy shows up in 'banana'. The relation 'u encounters w' is transitive, and thus generates ... 
Extremal Infinite OverlapFree Binary Words
(The Electronic Journal of Combinatorics, 19980503)Let t be the infinite fixed point, starting with 1, of the morphism μ:0→01, 1→10. An infinite word over {0,1} is said to be overlapfree if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ... 
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 ... 
Avoiding Patterns in the Abelian Sense
(Canadian Mathematical Society, 200108)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 ... 
NonRepetitive Tilings
(The Electronic Journal of Combinatorics, 20020703)In 1906 Axel Thue showed how to construct an infinite nonrepetitive (or squarefree) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a twodimensional ... 
There are Ternary Circular SquareFree Words of Length n for n ≥ 18
(The Electronic Journal of Combinatorics, 20021011)There are circular squarefree words of length n on three symbols for n≥18. This proves a conjecture of R. J. Simpson. 
Counting endomorphisms of crownlike orders
(Springer, 200212)The authors introduce the notion of crownlike orders and introduce powerful tools for counting the endomorphisms of orders of this type. 
There Exist Binary Circular 5/2+ Power Free Words of Every Length
(The Electronic Journal of Combinatorics, 20040123)We show that there exist binary circular 5/2+ power free words of every length. 
The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially
(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} 
Attainable lengths for circular binary words avoiding kpowers
(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 
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 20060922)We characterize the squares occurring in infinite overlapfree binary words and construct various α powerfree binary words containing infinitely many overlaps. 
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 ... 
For each a > 2 there is an Infinite Binary Word with Critical Exponent a
(The Electronic Journal of Combinatorics, 20080831)The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an αpower. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ...