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The paper presents a counterexample to the Hodge conjecture.

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We give a counterexample to a recently conjectured variant of the Penrose inequality.

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In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

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In this paper, we give a simple counter example to the famous Hodge conjecture.

General Mathematics · Mathematics 2013-01-23 Renyi Ma

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

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The article presents the proof of Casas-Alvero conjecture.

Number Theory · Mathematics 2017-05-09 Edward Dobrowolski

New cases of the multiplicity conjecture are considered.

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A conjecture of Woods from 1972 is disproved.

Number Theory · Mathematics 2017-10-18 Oded Regev , Uri Shapira , Barak Weiss

In this paper we prove the WALA conjecture.

Metric Geometry · Mathematics 2026-05-29 Andrea Merlo

In this short note we present a family of counterexamples to the King's conjecture.

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We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

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In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

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

Number Theory · Mathematics 2020-09-09 Tibor Burdette , Ian Stewart

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

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In this paper, we prove a conjecture of Schnell in the surface case.

Algebraic Geometry · Mathematics 2024-02-27 Jun Lu , Wan-Yuan Xu

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

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We prove a recent conjecture by Ulas on reducible polynomial substitutions.

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We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

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We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

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