4 citations · 14 across the 23 of their papers we have counts for
29 papers
Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
Alessio Figalli, Peter van Hintum, Marius Tiba
The Borell-Brascamp-Lieb inequality is a classical extension of the Prékopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The st…
Upper bounds for multicolour Ramsey numbers
Paul Balister, Béla Bollobás, Marcelo Campos +5
The -colour Ramsey number is the minimum such that every -colouring of the edges of the complete graph on vertices contains a monochroma…
Intersections of iterated shadows
Hou Tin Chau, David Ellis, Marius Tiba
We show that if with measure bounded away from zero and from one, then the -iterated upper shadows of and $\mathc…
Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
Alessio Figalli, Peter van Hintum, Marius Tiba
The Brunn-Minkowski inequality, applicable to bounded measurable sets and in , states that . Equality is achieved if and…
Sharp quantitative stability of the Brunn-Minkowski inequality
Alessio Figalli, Peter van Hintum, Marius Tiba
The Brunn-Minkowski inequality states that for bounded measurable sets and in , we have . Also, equality holds if and on…
Random Translates in Minkowski Sums
Paul Balister, Bela Bollobas, Imre Leader +1
Suppose that and are sets in , and we form the sumset of with random points of . Given the volumes of and , how should we choose them to min…
On Ruzsa's discrete Brunn-Minkowski conjecture
Peter van Hintum, Peter Keevash, Marius Tiba
We prove a conjecture by Ruzsa from 2006 on a discrete version of the Brunn-Minkowski inequality, stating that for any and with not contained in…
Erdős covering systems
Paul Balister, Béla Bollobás, Robert Morris +2
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the foll…
Towards Hadwiger's conjecture via Bourgain Slicing
Marcelo Campos, Peter van Hintum, Robert Morris +1
In 1957, Hadwiger conjectured that every convex body in can be covered by translates of its interior. For over 60 years, the best known bound was of the form $…
Large sumsets from medium-sized subsets
Bela Bollobas, Imre Leader, Marius Tiba
The classical Cauchy--Davenport inequality gives a lower bound for the size of the sum of two subsets of , where is a prime. Our main aim in this paper is to pro…
Large sumsets from small subsets
Bela Bollobas, Imre Leader, Marius Tiba
In this paper we start to investigate a new body of questions in additive combinatorics. The fundamental Cauchy--Davenport theorem gives a lower bound on the size of a sumset A+B f…
A strengthening of Freiman's 3k-4 theorem
Bela Bollobas, Imre Leader, Marius Tiba
In its usual form, Freiman's 3k-4 theorem states that if A and B are subsets of the integers of size k with small sumset (of size close to 2k) then they are very close to arithmeti…
Radius, Girth and Minimum Degree
Vojtěch Dvořák, Peter van Hintum, Amy Shaw +1
Given a connected graph on vertices, with minimum degree and girth at least , what is the maximum radius this graph can have? Erdős, Pach, Pollack a…
Sharp L1 Inequalities for Sup-Convolution
Peter van Hintum, Hunter Spink, Marius Tiba
Given a compact convex domain and bounded measurable functions , define the sup-convolution t…
Improved Bound for Tomaszewski's Problem
Vojtěch Dvořák, Peter van Hintum, Marius Tiba
In 1986, Tomaszewski made the following conjecture. Given real numbers with , then of the signed sums $\pm a_{1} \pm ... \p…
Sets in with doubling are near convex progressions
Peter van Hintum, Hunter Spink, Marius Tiba
For sufficiently small and with , we show either is covered by parallel hyperplanes, or satisfies $|\widehat{\operat…
Sharp quantitative stability of the planar Brunn-Minkowski inequality
Peter van Hintum, Hunter Spink, Marius Tiba
We prove a sharp stability result for the Brunn-Minkowski inequality for . Assuming that the Brunn-Minkowski deficit $δ=|A+B|^{\frac{1}{2}}/(|A|^\frac12+|B|…
Flat Littlewood Polynomials Exist
Paul Balister, Béla Bollobás, Robert Morris +2
We show that there exist absolute constants such that, for all , there exists a polynomial of degree , with coefficients, such that $$δ\sqrt…
Sharp Stability of Brunn-Minkowski for Homothetic Regions
Peter van Hintum, Hunter Spink, Marius Tiba
We prove a sharp stability result concerning how close homothetic sets attaining near-equality in the Brunn-Minkowski inequality are to being convex. In particular, resolving a con…
Multicolour chain avoidance in the boolean lattice
Hunter Spink, Marius Tiba
Given a collection of colored chain posets, we estimate the number of colored subsets of the boolean lattice which avoid all chains in the collection.
The structure and number of Erdős covering systems
Paul Balister, Béla Bollobás, Robert Morris +2
Introduced by Erdős in 1950, a covering system of the integers is a finite collection of arithmetic progressions whose union is the set . Many beautiful questions and c…
The Erdős-Selfridge problem with square-free moduli
Paul Balister, Béla Bollobás, Robert Morris +2
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in…
On the Erdős Covering Problem: the density of the uncovered set
Paul Balister, Béla Bollobás, Robert Morris +2
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and nume…
Judiciously 3-partitioning 3-uniform hypergraphs
Hunter Spink, Marius Tiba
Bollobás, Reed and Thomason proved every -uniform hypergraph with edges has a vertex-partition such that each part m…