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Class Numbers and Biquadratic Reciprocity
(Cambridge University Press, 1982)
The number of order–preserving maps of fences and crowns
(Springer, 1991-06)
We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results.
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.
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 ...
Suffix conjugates for a class of morphic subshifts
(Cambridge University Press, 2015-09)
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and ...
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.
Non-Repetitive Tilings
(The Electronic Journal of Combinatorics, 2002-07-03)
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...
Avoidability index for binary patterns with reversal
(2017)
For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.
A direct proof of a result of Thue
(Utilitas Mathematica, 1984)
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.