Related papers: Counterexamples to a conjecture of Woods

The rank of tensors is not additive with respect to the direct sum.

Brandt et al. (2013) have recently disproved a conjecture by Schwartz (1990) by non-constructively showing the existence of a counterexample with about 10^136 alternatives. We provide a concrete counterexample for Schwartz's conjecture with…

We prove the Aharoni Berger Conjecture

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

We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets $A \subset \mathbb{N}$ with the property that $\mathbb{N} \setminus A$ is infinite, but the sequence $n \rightarrow |\{ (a,b,c) \,…

We provide a simple explicit counterexample to a group completion conjecture for simplicial monoids attributed to JC Moore.

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.

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

In this short note we give counterexamples to several results related to extension theorems published recently.

For $n \geq 2$ we construct a measurable subset of the unit ball in $\mathbb{R}^n$ that does not contain pairs of points at distance 1 and whose volume is greater than $(1/2)^n$ times the volume of the ball. This disproves a conjecture of…

Several results about the union-closed sets conjecture are presented.

Recently, a conjecture due to Hendry was disproved which stated that every Hamiltonian chordal graph is cycle extendible. Here we further explore the conjecture, showing that it fails to hold even when a number of extra conditions are…

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

An old conjecture of Durfee 1978 bounds the ratio of two basic invariants of complex isolated complete intersection surface singularities: the Milnor number and the singularity (or geometric) genus. We give a counterexample for the case of…

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…

We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.

The article presents the proof of Casas-Alvero conjecture.

Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.

Although false for general graphs, this note gives an elementary proof of the bunkbed conjecture for any acyclic graph. The argument is short and self-contained, and may be of educational interest.

We prove Simon's conjecture for 3-manifolds.