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

This paper has been withdrawn by the author due to errors.

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

This paper has been withdrawn.

This paper has been withdrawn by the authors due to a more research needed to estimate $h^{*}_{n}(b)$ which really should be written as $h^{*}_{n}(b,A)$ for $b\in \Gamma (t)$.

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $\Theta(n^2)$ distinct factors, and there exist words of length $n$ containing $\Theta(n^2)$ distinct…

For permutations avoiding consecutive patterns from a given set, we present a combinatorial formula for the multiplicative inverse of the corresponding exponential generating function. The formula comes from homological algebra…

This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.

This paper has been withdrawn due to a crucial error in the proof of the main theorem

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

Building an infinite square-free word by appending one letter at a time while simultaneously avoiding the creation of squares is most likely to fail. When the alphabet has two letters this approach is impossible. When the alphabet has three…

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

We construct an infinite word $w$ over the $5$-letter alphabet such that for every factor $f$ of $w$ of length at least two, there exists a cyclic permutation of $f$ that is not a factor of $w$. In other words, $w$ does not contain a…

The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.

Word Embeddings have been shown to contain the societal biases present in the original corpora. Existing methods to deal with this problem have been shown to only remove superficial biases. The method of Adversarial Debiasing was presumed…

This paper has been withdrawn due to a error in Theorem 3.1.

This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.

Carpi constructed an infinite word over a 4-letter alphabet that avoids squares in all subsequences indexed by arithmetic progressions of odd difference. We show a connection between Carpi's construction and the paperfolding words. We…

We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of…

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…