Counting abelian squares.
Unbounded discrepancy in Frobenius numbers.
Weakly self-avoiding words and a construction of Friedman.
On minimal words with given subword complexity.
Binary words containing infinitely many overlaps.
Sums of digits, overlaps, and palindromes.
The cycles of the multiway perfect shuffle permutation.
Automaticity IV : sequences, sets, and diversity
This paper studies the descriptional complexity of (i) sequences over a finite alphabet ; and (ii) subsets of (the natural numbers). If is a sequence over a finite alphabet , then we define the - of , to be the smallest possible number of states in any deterministic finite automaton that, for all with , takes expressed in base as input and computes . We give examples of sequences that have high automaticity in all bases ; for example, we show that the characteristic sequence of...
Extremal infinite overlap-free binary words.
Van der Waerden's theorem and avoidability in words.
Morphic and automatic words: maximal blocks and Diophantine approximation
Correction to : “Linear fractional transformations of continued fractions with bounded partial quotients”
We fill a gap in the proof of a theorem of our paper cited in the title.
Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde
Nous montrons que le tracé d’un kolam indien classique, que l’on retrouve aussi dans la tradition des dessins sur le sable aux îles Vanuatu, peut être engendré par un morphisme de monoïde. La suite infinie morphique ainsi obtenue est reliée à la célèbre suite de Prouhet-Thue-Morse, mais elle n’est -automatique pour aucun entier .
Squares and overlaps in the Thue-Morse sequence and some variants
We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are -regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of ) contains an overlap.
Convergents of folded continued fractions
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