相关论文: Counterexamples to a conjecture of Woods

In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture.

We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.

This paper has been withdrawn by the authors due to an error in Section 7.

We exhibit examples of projective varieties with degenerate Gauss mappings and determine numerical invariants of such varieties. Our examples provide counter-examples to an asserted structure theorem of Griffiths and Harris (Ann. Sci. ENS…

New cases of the multiplicity conjecture are considered.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We prove that a strong version of Chang's Conjecture, equivalent to the Weak Reflection Principle at $\omega_2$, together with $2^\omega=\omega_2$, imply there are no $\omega_2$-Aronszajn trees.

We show that the analogue of the Peterson conjecture on the action of Steenrod squares does not hold in motivic cohomology.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

General considerations on the Equivalence conjectures and a review of few mathematical results.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J.…

This is a reformulation and refutation of a proposed proof of the Riemann hypothesis published in 2013 (arXiv:1305.0323) and in 2014 (arXiv:1402.2822). Proceeding by contradiction, the author wants to prove that if zeta(s)=0 where 1/2<Re…

We provide various counter-examples to the long-standing so-called "Omnibus Conjecture" in Rational Homotopy Theory. That is, we show that a space with finite dimensional even-degree rational cohomology and finite dimensional spherical…

We give counterexamples to the Brown-Colbourn conjecture on reliability polynomials, in both its univariate and multivariate forms. The multivariate Brown-Colbourn conjecture is false already for the complete graph K_4. The univariate…

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and…

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

The paper disproves a basic theorem on quasi-birth-and-death processes given in [M. F. Neuts (1995). Matrix Geometric Solutions in Stochastic Models: An Algorithmic Approach. Dover, New York].