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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.
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 ...
Square-free Words with Square-free Self-shuffles
(The Electronic Journal of Combinatorics, 2014-01-12)
We answer a question of Harju: For every n ≥ 3 there is a square-free ternary word of length n with a square-free self-shuffle.
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 best-known 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 ...
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 ...
Self-Complementary Hypergraphs
(University of Ottawa, 2009)
In this thesis, we survey the current research into self-complementary 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 ...
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 ...
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 ...
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 ...