Related papers: A short note on Godbersen's Conjecture

We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…

We give lower bounds on the case of worst inhomogeneous approximation.

We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such…

Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

We prove some extensions of Andrews inequality.

We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We improve the previuosly known bound for some vertex Folkman numbers.

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

We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp(1.96 \times 10^{19})$, which is significantly below the conjectured value of $\approx \exp(5.15 \times…

In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.

We provide new sufficient conditions under which Ryser's conjecture holds.

Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…

In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.

In this paper we provide a Bonnesen-style inequality which gives a lower bound for the isoperimetric deficit corresponding to a closed convex curve in terms of some geometrical invariants of this curve. Moreover we give a geometrical…

We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…