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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}
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 ...
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.
This is Us: Latent Profile Analysis of Canadian Teachers’ Burnout during the COVID-19 Pandemic
(Canadian Society for the Study of Education, 2022)
During the initial wave of the COVID-19 pandemic, 1,930 Canadian teachers were surveyed about their burnout and resilience levels, as well as their job demands and resources. Latent profile analysis revealed that teachers ...
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.
Overlap-Free Words and Generalizations
(University of Winnipeg, 2007)
The study of combinatorics on words dates back at least to the beginning of the
20th century and the work of Axel Thue. Thue was the first to give an example of an infinite word over a three letter alphabet that contains ...
Vertex-transitive self-complementary uniform hypergraphs of prime order
(Discrete Mathematics, 2009-09)
For an integer n and a prime p, let n(p)=max{i:pidividesn}. In this paper, we present a construction for vertex-transitive self-complementary k-uniform hypergraphs of order n for each integer n such that pn(p)≡1(mod2ℓ+1) ...
Transformational Leadership Approaches and Their Influence on Teacher Resilience During the COVID-19 Pandemic
(North American Business Press, 2022)
With stress documented beyond inherent levels in our initial research with Canadian teachers during the COVID-19 pandemic, this case study moves beyond the consideration of individual strategies to reduce burnout, toward ...
A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba
(The Electronic Journal of Combinatorics, 2016-05-27)
We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we characterize ...