Related papers: Counterexamples to a conjecture of Woods
In this paper, we give a simple counter example to the famous Hodge conjecture.
The paper presents a counterexample to the Hodge conjecture.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this short note I restate and simplify the proof of the impossibility of probabilistic induction from Popper (1992). Other proofs are possible (cf. Popper (1985)).
We present counterexamples to a 30-year-old conjecture of Las Vergnas [J. Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.
In this note, we disprove two Romanov type conjectures posed by Chen.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
In this article, we give two different proofs of why the Collatz Conjecture is false.
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of Hollom (2024).
Paper withdrawn by the author.
Two conjectures recently proposed by one of the authors are disproved
In this short note we present a family of counterexamples to the King's conjecture.
In this paper, the abc conjecture is negated under certain conditions
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576
In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.