Related papers: There are exponentially many ternary words that av…

A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance p match. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of…

This paper has been withdrawn as the statements in Proposition 4.4 and Theorem 1.4(i) are not correct.

This paper has been withdrawn by the authors due to an error in Section 7.

This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.

This paper has been withdrawn by the author due to a crucial error in the last lines in the proof of Lemma 3.3.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

The notion of Abelian complexity of infinite words was recently used by the three last authors to investigate various Abelian properties of words. In particular, using van der Waerden's theorem, they proved that if a word avoids Abelian…

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing…

We study words that barely avoid repetitions, for several senses of "barely". A squarefree (respectively, overlap-free, cubefree) word is irreducible if removing any one of its interior letters creates a square (respectively, overlap,…

This paper has been withdrawn due to an error in the proof of Theorem 5.3.

In this paper we examine the possibility of describing omitting types 1 and 2 by two at most ternary terms and any number of linear identities. All possible cases of systems of linear identities on two at most ternary terms are being…

We consider avoiding mesosomes -- that is, words of the form $xx'$ with $x'$ a conjugate of $x$ that is different from $x$ -- over a binary alphabet. We give a structure theorem for mesosome-avoiding words, count how many there are,…

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

A celebrated theorem by Coven and Hedlund (1973) states that Sturmian words are characterized by their abelian complexity: they are precisely the infinite words with rationally independent letter frequencies and constant abelian complexity…

The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of…

This paper has been withdrawn by the author, due to a crucial error in page 5.

Fici and Saarela ([2]) conjectured that a binary word of length n contains at least $\lfloor n/4 \rfloor$ abelian squares. We slightly extend this conjecture and show that it holds in some special cases. In all other cases we have the…

The paper is withdrawn.

An infinte word w avoids a pattern p with the involution t if there is no substitution for the variables in p and no involution t such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the…

This paper has been withdrawn by the author due to a crucial error in equation (51).