Related papers: On Ryser's Conjecture

We prove Union-Closed sets conjecture.

We use the Taylor-Wiles-Kisin patching method to prove some new cases of the Breuil-Schneider conjecture.

In a previous paper, we studied certain sequences of simultaneous rational approximations in ${\bf R}^2$ which present some analogy with the continued fractions. We got results around the Littlewood conjecture by using such approximations.…

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

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

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

The paper presents a counterexample to the Hodge conjecture.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We prove necessary and sufficient conditions for the validity of Whitney's extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity.

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

We provide conjectural necessary and (separately) sufficient conditions for the Hilbert scheme of points of a given length to have the maximum dimension tangent space at a point. The sufficient condition is claimed for 3D and reduces the…

New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.

A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…

In this paper the circulant Hadamard conjecture is proved.

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

The intensity of debate between the realists and antirealists shows no sign of abating. Here a new hypothesis is proposed to resolve the issue. The requirement of consistency and continuity are built-in in the methodology of this…