Now showing items 1-10 of 20
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 ...
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 ...
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.
(The Electronic Journal of Combinatorics, 2002-07-03)
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...
Least Periods of Factors of Infinite Words
(EDP Sciences, 2009)
We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ...
Sliding Down Inclines with Fixed Descent Time: a Converse to Galileo's Law of Chords
(Canadian Mathematical Society, 2008-12)
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
Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics
This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323–1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite ...
Regular Two-Graphs and Equiangular Lines
(University of Winnipeg, 2004)
Regular two-graphs are antipodal distance-regular double coverings of the complete graph, and they have many interesting combinatorial properties. We derive a construction for regular two-graphs containing cliques of ...
There Exist Binary Circular 5/2+ Power Free Words of Every Length
(The Electronic Journal of Combinatorics, 2004-01-23)
We show that there exist binary circular 5/2+ power free words of every length.