Department of Mathematics and Statistics
http://hdl.handle.net/10680/289
2019-07-16T14:06:25ZSuffix conjugates for a class of morphic subshifts
http://hdl.handle.net/10680/1703
Suffix conjugates for a class of morphic subshifts
Currie, James D.; Rampersad, Narad; Saari, Kalle
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and T: X --> X is the shift map. Let S be a finite alphabet that is in bijective correspondence via a mapping c with the set of nonempty suffixes of the images f(a) for a in A. Let calS be a subset S^N be the set of infinite words s = (s_n)_{n\geq 0} such that \pi(s):= c(s_0)f(c(s_1)) f^2(c(s_2))... is in X. We show that if f is primitive and f(A) is a suffix code, then there exists a mapping H: calS --> calS such that (calS, H) is a topological dynamical system and \pi: (calS, H) --> (X, T) is a conjugacy; we call (calS, H) the suffix conjugate of (X, T). In the special case when f is the Fibonacci or the Thue-Morse morphism, we show that the subshift (calS, T) is sofic, that is, the language of calS is regular.
2015-09-01T00:00:00ZA Characterization of Fractionally Well-Covered Graphs
http://hdl.handle.net/10680/1701
A Characterization of Fractionally Well-Covered Graphs
Currie, James; Nowakowski, Richard
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 that for every vertex the sum of all the weights in its closed neighbourhood be at least 1. In this paper we consider and characterize fractionally well-covered graphs.
1991-01-01T00:00:00ZAvoiding Patterns in the Abelian Sense
http://hdl.handle.net/10680/1699
Avoiding Patterns in the Abelian Sense
Currie, J.; Linek, V.
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 properties of ω-words avoiding these patterns.
2001-08-01T00:00:00ZWords without Near-Repetitions
http://hdl.handle.net/10680/1697
Words without Near-Repetitions
Currie, J.; Bendor-Samuel, A.
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 y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.
1992-06-01T00:00:00ZA direct proof of a result of Thue
http://hdl.handle.net/10680/1696
A direct proof of a result of Thue
Currie, James D.
1984-01-01T00:00:00ZThe Complexity of the Simplex Algorithm
http://hdl.handle.net/10680/1695
The Complexity of the Simplex Algorithm
Currie, James
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 of Klee-Minty programs, the behaviour of the Simplex algorithm is only good on average. To take such an average, certain assumptions on the distribution of linear programs are introduced and discussed.
A geometrical meaning is given for the number of steps Lemke's algorithm takes to solve a program. This gives rise to a formula bounding the average number of steps taken. This formula is heuristically justified in an original way.
The formula is combinatorially simplified, to get a bound on the complexity of Simplex.
1984-08-01T00:00:00ZClass Numbers and Biquadratic Reciprocity
http://hdl.handle.net/10680/1694
Class Numbers and Biquadratic Reciprocity
Williams, Kenneth S.; Currie, James D.
The research of the first author was supported by Natural Sciences and Engineering Research Council Canada Grant No. A-7233, while that of the second was supported by a Natural Sciences and Engineering Research Council Canada Undergraduate Summer Research Award.
1982-01-01T00:00:00ZNon repetitive walks in graphs and digraphs
http://hdl.handle.net/10680/1654
Non repetitive walks in graphs and digraphs
Currie, James Daniel
A word $w$ over alphabet $\Sigma$ is {\em non-repetitive} 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 theorist, showed that arbitrarily long non-repetitive words exist on a three letter alphabet.
Call a graph or digraph $G$ {\em versatile} if arbitrarily long non-repetitive words can be walked on $G$. This work deals with two questions:
\begin{enumerate}
\item Which graphs are versatile?
\item Which digraphs are versatile?
\end{enumerate}
Our results concerning versatility of digraphs may be considered to give information about the structure of non-repetitive words on finite alphabets.
We attack these questions as follows:
\begin{enumerate}
\item We introduce a partial order on digraphs called {\em mimicking}. We show that if digraph $G$ mimics digraph $H$, then if $H$ is versatile, so is $G$.
\item We then produce two sets of digraphs MIN and MAX, and show that every digraph of MIN is versatile. (These digraphs are intended to be minimal in the mimicking partial order with respect to being versatile.) and no digraph of MAX is versatile. (The digraphs of MAX are intended to be maximal with respect to not being versatile.)
\item In a lengthy classification, we show that every digraph either mimics a digraph of MIN, and hence is versatile, or "reduces" to some digraph mimicked by a digraph of MAX, and hence is not versatile.
We conclude that a digraph is versatile exactly when it mimics one of the digraphs in the finite set MIN. The set MIN contains eighty-nine (89) digraphs, and the set MAX contains twenty-five (25) individual digraphs, and one infinite family of digraphs.
\end{enumerate}
PhD thesis of James Daniel Currie (University of Calgary, 1987)
1987-06-01T00:00:00ZSkeleton Cave, Leigh Woods, Bristol
http://hdl.handle.net/10680/1578
Skeleton Cave, Leigh Woods, Bristol
Mullan, G. J.; Meiklejohn, C.; Babb, J.
An account is given of the discovery and excavation of this small cave in the 1960s. It is recorded that archaeological finds were made, but of these, only a single human mandible can now be traced. Radiocarbon dating shows the specimen to be early Neolithic in age; a metrical analysis was less conclusive.
2017-01-01T00:00:00ZIntroduction: Special volume in honor of Jeffrey Shallit on the occasion of his 60th birthday
http://hdl.handle.net/10680/1419
Introduction: Special volume in honor of Jeffrey Shallit on the occasion of his 60th birthday
Rampersad, Narad
2018-03-01T00:00:00Z