相关论文: Counterexamples to a conjecture of Woods

In this note, we show that a "Toy Conjecture" made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full ("non-toy") conjecture in that work, and it is our hope that this note will…

We prove Union-Closed sets conjecture.

We survey recent developments on the Restriction conjecture.

We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…

Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.

A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.

We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even…

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

We argue that the conclusion about the invalidity of the Dirac conjecture, made in the paper by Wang, Li, and Wang (Int. J. Theor. Phys. 48 1894, 2009), was based upon a flawed analysis of the proposed counterexamples. In the case of the…

This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

Error in proof of theorem 10.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

A proof of Sendov's conjecture is given.

The said paper [Su2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is false.

We show the Williams Conjecture is false for irreducible shifts of finite type by examining relative sign-gyration numbers of conjugacies between shifts with no points of period one or two.

It is shown that the arguments in the reply of Z.-D. Zhang (arXiv:0812.0194) to the comment arXiv:0811.1802 defending his conjectures in arXiv:0705.1045 are invalid. His conjectures have been thoroughly disproved.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.