Results 1 
5 of
5
Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.
A characterization of 2+free words over a binary alphabet
, 1995
"... It is shown that 2+repetition, i.e. a word of the form uvuvu where u is a letter and v is a word, is the smallest repetition which can be avoided in infinite words over binary alphabet. Such binary words avoiding pattern uvuvu, finite or infinite, are called as 2+free words and those words are the ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
It is shown that 2+repetition, i.e. a word of the form uvuvu where u is a letter and v is a word, is the smallest repetition which can be avoided in infinite words over binary alphabet. Such binary words avoiding pattern uvuvu, finite or infinite, are called as 2+free words and those words are the main topic of this work. It is shown here that 2+free words over binary alphabet can be presented as words built from special kind of blocks, called Morseblocks, with some rules. In particular, the given presentation by these blocks is unique for 2+free words long enough. Moreover, it is also shown that the language generated by this presentation can be described by some automaton. In fact, the corresponding presentation in blocks for finite 2
Border correlation of binary words
 J. Combin. Theory Ser. A
"... The border correlation function β: A ∗ → A ∗ , for A = {a, b}, specifies which conjugates (cyclic shifts) of a given word w of length n are bordered, in other words, β(w) = c0c1... cn−1, where ci = a or b according to whether the ith cyclic shift σ i (w) of w is unbordered or bordered. Except for ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The border correlation function β: A ∗ → A ∗ , for A = {a, b}, specifies which conjugates (cyclic shifts) of a given word w of length n are bordered, in other words, β(w) = c0c1... cn−1, where ci = a or b according to whether the ith cyclic shift σ i (w) of w is unbordered or bordered. Except for some special cases, no binary word w has two consecutive unbordered conjugates (σ i (w) and σ i+1 (w)). We show that this is optimal: in every cyclically overlapfree word every other conjugate is unbordered. We also study the relationship between unbordered conjugates and critical points, as well as, the dynamic system given by iterating the function β. We prove that, for each word w of length n, the sequence w, β(w), β 2 (w),... terminates either in b n or in the cycle of conjugates of the word ab k ab k+1 for n = 2k + 3.