Search
Now showing items 21-30 of 39
A Characterization of Fractionally Well-Covered Graphs
(Ars Combinatoria, 1991)
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 ...
Infinite words containing squares at every position
(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 α-powers but contains arbitrarily large squares beginning at every position? We resolve ...
Extremal Infinite Overlap-Free Binary Words
(The Electronic Journal of Combinatorics, 1998-05-03)
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 overlap-free if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ...
Avoidability index for binary patterns with reversal
(The Electronic Journal of Combinatorics, 2016-02-19)
For every pattern p over the alphabet {x, x^R, y, y^R}, we specify the least k such that p is k-avoidable.
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 ...
Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1
(Integers, 2014-02-20)
We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds ...
Avoiding three consecutive blocks of the same size and same sum
(Association of Computing Machinery, 2014-04)
We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994.
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 ...