## Search

Now showing items 1-10 of 27

#### 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 ...

#### 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.

#### Class Numbers and Biquadratic Reciprocity

(Cambridge University Press, 1982)

#### 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.

#### 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 ...

#### Extremal Infinite Overlap-Free Binary Words

(The Electronic Journal of Combinatorics, 1998-05-03)

Let t be the infinite fixed point, starting with 1, of the morphism μ:0→01, 1→10. An infinite word over {0,1} is said to be overlap-free if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ...

#### 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.

#### A Note on Antichains of Words

(The Electronic Journal of Combinatorics, 1995-10-14)

We can compress the word 'banana' as xyyz, where x= 'b', y= 'an',z= 'a'. We say that 'banana' encounters yy. Thus a 'coded' version of yy shows up in 'banana'. The relation 'u encounters w' is transitive, and thus generates ...