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Publications associées (42)

Multiplicative combinatorial properties of return time sets in minimal dynamical systems

We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove t ...

2019

A proof of a sumset conjecture of Erdős

Florian Karl Richter

In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured ...

2019

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Lonely Runner Polyhedra

Matthias Schymura

We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...

2018

Decomposition of Multiple Packings with Subquadratic Union Complexity

János Pach, Bartosz Maria Walczak

Suppose k is a positive integer and X is a k-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most k sets. Suppose there is a function f(n) = o(n(2)) with the property that any ...

Cambridge Univ Press2016

Unsplittable Coverings in the Plane

János Pach

A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of its members. A 1-fold covering is called a covering. The problem of splitting multiple coverings into several coverings was motivated by classical density est ...

Springer-Verlag Berlin2016

Unsplittable coverings in the plane

János Pach

Academic Press Inc Elsevier Science2016

Simultaneous Approximation of Polynomials

János Pach, Andrei Kupavskii

Let P-d denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers x(1)

Springer Int Publishing Ag2016

Time-Varying Gaussian Process Bandit Optimization

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. ...

2016

The number of double-normals in space

Andrei Kupavskii

Given a set V of points in , two points p, q from V form a double-normal pair, if the set V lies between two parallel hyperplanes that pass through p and q, respectively, and that are orthogonal to the segment pq. In this paper we study the maximum number ...

Springer2016

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