Related papers: Skew characters which contain only few components

This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas

The paper has been withdrawn, since there is a mistake in Proposition 5.2. The result on the telescope conjecture for semihereditary rings is correct, but the characterization of the smashing subcategories of the derived category of…

The paper was withdrawn due to a gap in the proof of Lemma 3.

The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its "proof" is not correct. Here we change the statements and proofs of Lemma…

Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand,…

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must…

This paper has been withdrawn due to a error in Theorem 3.1.

This paper has been withdrawn by the author. Lemma 8 is used in the proof of Lemma 6, but it is not correct. Lemma 6 is essential for the main results.

This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.

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…

This text highlights issues present in the proof of Lemma 6.10 of the Baumgartner (1943 -- 2011) article "Almost disjoint sets, the dense set problem and the partition calculus" of 1976, and intends to present a correction at the same time…

We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.

It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in error and violates well-known theorems.

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

Let $so_3(K)$ be the Lie algebra of $3\times 3$ skew-symmetric matrices over a field $K$ of characteristic 0. The ideal $I(M_3(K),so_3(K))$ of the weak polynomial identities of the pair $(M_3(K),so_3(K))$ consists of the elements…

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

The proof of Lemma 5.1 in the paper Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups (J. Topol. 16 (2023), no. 2, 634--649) is incomplete as it relies on some results of Choudhury-Hagadi,…

The main result is a direct proof of the implication $(LVKF_{k,3})\Rightarrow( LT_{3k-1,3})$ below. Consider the following statements: ($LVKF_{1,3}$) From any 11 points in $ \mathbb{R}^{3}$ one can choose 3 pairwise disjoint triples whose…

We design and conduct a simple experiment to study whether neural networks can perform several steps of approximate reasoning in a fixed dimensional latent space. The set of rewrites (i.e. transformations) that can be successfully performed…

Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. Lower bounds for random 3CNF refutations in many propositional proof systems are known. Most notably are the…