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

This paper has been withdrawn by the authors, due to an error in the proof of Lemma 3.1.

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2

We present a new approach to ternary Boolean algebras in which negation is derived from the ternary operation. The key aspect is the replacement of complete commutativity by other axioms that do not require the ternary operation to be…

This paper has been withdrawn by the author, due to errors in the figures.

This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments…

A square-free word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ (at any position) contains a square. Grytczuk et al. recently introduced the concept of extremal…

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

This paper concerns the avoidability of abelian and additive powers in infinite rich words. In particular, we construct an infinite additive $5$-power-free rich word over $\{0,1\}$ and an infinite additive $4$-power-free rich word over…

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

The article has been withdrawn by the author due to the existence of counterexamples.

This paper has been withdrawn

This paper has been withdrawn

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

This paper has been withdrawn by the author.

We prove that the multiplicities of certain maximal weights of $\mathfrak{g}(A^{(1)}_{n})$-modules are counted by pattern avoidance on words. This proves and generalizes a conjecture of Misra-Rebecca. We also prove similar phenomena in…

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.