Browsing Department of Mathematics and Statistics by Issue Date
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Squares and overlaps in the ThueMorse sequence and some variants
(EDP Sciences, 2006)We consider the position and number of occurrences of squares in the ThueMorse sequence, and show that the corresponding sequences are 2regular. We also prove that changing any finite but nonzero number of bits in the ... 
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 20060922)We characterize the squares occurring in infinite overlapfree binary words and construct various α powerfree binary words containing infinitely many overlaps. 
OverlapFree Words and Generalizations
(University of WinnipegUniversity of Waterloo, 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 ... 
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 ... 
For each a > 2 there is an Infinite Binary Word with Critical Exponent a
(The Electronic Journal of Combinatorics, 20080831)The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an αpower. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ... 
Sliding Down Inclines with Fixed Descent Time: a Converse to Galileo's Law of Chords
(Canadian Mathematical Society, 200812) 
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. 
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 ThueMorse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ... 
SelfComplementary Hypergraphs
(University of OttawaUniversity of Ottawa and Carleton University (joint program), 2009)In this thesis, we survey the current research into selfcomplementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which ... 
Vertextransitive selfcomplementary uniform hypergraphs of prime order
(Discrete Mathematics, 200909)For an integer n and a prime p, let n(p)=max{i:pidividesn}. In this paper, we present a construction for vertextransitive selfcomplementary kuniform hypergraphs of order n for each integer n such that pn(p)≡1(mod2ℓ+1) ... 
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 αpowers but contains arbitrarily large squares beginning at every position? We resolve ... 
Generating selfcomplementary uniform hypergraphs
(Discrete Mathematics, 201002)In 2007, Szymanski and Wojda proved that for positive integers n; k with k less than n, a selfcomplementary kuniform hypergraph of order n exists if and only if n/k is even. In this paper, we characterize the cycle type ... 
Cyclically tcomplementary uniform hypergraphs
(European Journal of Combinatorics, 201005)A cyclically tcomplementary khypergraph is a kuniform 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 ... 
Multidimensional sets recognizable in all abstract numeration systems
(EDP Sciences, 2011)We prove that the subsets of Nd that are Srecognizable for all abstract numeration systems S are exactly the 1recognizable sets. This generalizes a result of Lecomte and Rigo in the onedimensional setting. 
Constructing Regular Selfcomplementary Uniform Hypergraphs
(Journal of Combinatorial Designs, 20110217)In this paper, we examine the possible orders of tsubsetregular selfcomplementary kuniform hypergraphs, which form examples of large sets of two isomorphic tdesigns. We reformulate Khosrovshahi and TayfehRezaie's ... 
Further applications of a power series method for pattern avoidance
(The Electronic Journal of Combinatorics, 20110621)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 nonerasing morphism h from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ... 
The minimal automaton recognizing mN in a linear numeration system
(Integers, 20111202)We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component ... 
The Aveline's Hole 9 Cranium: A Partial Solution to a Long Standing Enigma
(University of Bristol Spelaeological Society, 2012)Aveline's Hole is both one of the bestknown sites with early human skeletal material in Britain and one of the most problematic in its history. First discovered and explored at the close of the 18th century, it yielded ... 
Shuffling and unshuffling
(Bulletin of the European Association for Theoretical Computer Science, 2012)We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal ... 
Automaticity of Primitive Words and Irreducible Polynomials
(Discrete Mathematics and Theoretical Computer Science, 2013)If L is a language, the automaticity function AL(n) (resp. NL(n)) of L counts the number of states of a smallest deterministic (resp. nondeterministic) finite automaton that accepts a language that agrees with L on all ...