Search
Now showing items 1-10 of 19
Attainable lengths for circular binary words avoiding k-powers
(The Belgian Mathematical Society, 2005)
We show that binary circular words of length n avoiding 7/3+ powers exist
for every sufficiently large n. This is not the case for binary circular words
avoiding k+ powers with k < 7/3
Combinatorics and Algorithmics of Strings
(Dagstuhl Publishing, 2014-03-09)
Strings (aka sequences or words) form the most basic and natural data structure. They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words ...
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 ...
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 ...
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.
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.
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 ...
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.
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
(2015-09-14)
In previous work, Currie and Rampersad showed that the growth of the number
of binary words avoiding the pattern xxxR was intermediate between polynomial and
exponential. We now show that the same result holds for the ...
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 ...