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Now showing items 11-20 of 20
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 2006-09-22)
We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps.
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 ...
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.
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 ...
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
(2005)
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 ...
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 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}
Squares and overlaps in the Thue-Morse sequence and some variants
(EDP Sciences, 2006)
We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the ...