相关论文: There are exponentially many ternary words that av…

We study the avoidability of long $k$-abelian-squares and $k$-abelian-cubes on binary and ternary alphabets. For $k=1$, these are M\"akel\"a's questions. We show that one cannot avoid abelian-cubes of abelian period at least $2$ in infinite…

We introduce new avoidability problems for words by considering equivalence relations, k-abelian equivalences, which lie properly in between equality and commutative equality, i.e. abelian equality. For two k-abelian equivalent words the…

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

We obtain the following results about the avoidance of ternary formulas. Up to renaming of the letters, the only infinite ternary words avoiding the formula $ABCAB.ABCBA.ACB.BAC$ (resp. $ABCA.BCAB.BCB.CBA$) have the same set of recurrent…

We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider…

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

We completely characterize the words that can be avoided in infinite squarefree ternary words.

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.

We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| >= 4; our construction is somewhat simpler than the original…

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxx^R was intermediate between polynomial and exponential. We now show that the same holds for the growth of the number of…

Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement…

Entringer, Jackson, and Schatz conjectured in 1974 that every infinite cubefree binary word contains arbitrarily long squares. In this paper we show this conjecture is false: there exist infinite cubefree binary words avoiding all squares…

The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pattern avoiding permutations is adapted to words. As an…

This paper has been withdrawn by the author due to a crucial definition error of Triebel space.

The paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 7/3. More…