Browsing Department of Mathematics and Statistics by Title
Now showing items 21-40 of 73
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Constructing Regular Self-complementary Uniform Hypergraphs
(Journal of Combinatorial Designs, 2011-02-17)In this paper, we examine the possible orders of t-subset-regular self-complementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and Tayfeh-Rezaie's ... -
Counting endomorphisms of crown-like orders
(Springer, 2002-12)The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type. -
COVID-19’s Second Wave: How are teachers faring with the return to physical schools?
(Canadian Education Network, 2020-11-20) -
Cubefree words with many squares
(Discrete Mathematics and Theoretical Computer Science, 2014-05-13)We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n. -
Cyclic Complexity of Some Infinite Words and Generalizations
(Integers, 2018-03)Cassaigne et al. introduced the cyclic complexity function c_x(n), which gives the number of cyclic conjugacy classes of length-n factors of a word x. We study the behavior of this function for the Fibonacci word f and the ... -
Cyclically t-complementary uniform hypergraphs
(European Journal of Combinatorics, 2010-05)A cyclically t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation 2 Sym.V/ such that the sets E; E ; E 2; : : : ; E t1 partition the set of all ... -
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. -
A direct proof of a result of Thue
(Utilitas Mathematica, 1984) -
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 ... -
Extremal words in morphic subshifts
(Elsevier, 2014-01-22)Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order \sigma on A, we call the smallest word with respect to \sigma starting with b in the shift orbit closure of x an extremal word of ... -
A family of formulas with reversal of high avoidability index
(World Scientific, 2017)We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ... -
For each a > 2 there is an Infinite Binary Word with Critical Exponent a
(The Electronic Journal of Combinatorics, 2008-08-31)The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ... -
Further applications of a power series method for pattern avoidance
(The Electronic Journal of Combinatorics, 2011-06-21)In combinatorics on words, a word w over an alphabet ∑ is said to avoid a pattern p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ... -
Generating self-complementary uniform hypergraphs
(Discrete Mathematics, 2010-02)In 2007, Szymanski and Wojda proved that for positive integers n; k with k less than n, a self-complementary k-uniform hypergraph of order n exists if and only if n/k is even. In this paper, we characterize the cycle type ... -
Growth rate of binary words avoiding xxxR
(Elsevier, 2016-01)Abstract Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this ... -
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 ... -
It’s okay to be okay too. Why calling out teachers’ “toxic positivity” may backfire
(Canadian Education Network, 2020) -
Latent Profile Analysis of Manitoban Teachers' Burnout during the COVID-19 Pandemic
(University of Winnipeg, 2021-03) -
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 ...