52 citations · 127 across the 37 of their papers we have counts for
51 papers
Growth beyond exponent for convexity and iterated sum sets
Michalis Kokkinos, Oliver Roche-Newton
We prove that the bound \[ \max \{ |16A|,|16f(A)| \} \gg_m |A|^{\frac{3}{2}+\frac{1}{162}} \] holds for any polynomial with degree and any finite $A \subset \mathbb…
Geometric Sidon Problems
Felix Christian Clemen, Jakob Führer, Oliver Roche-Newton
This paper considers geometric problems of the following type: given a point set , one seeks a large subset avoiding a prescribed geometric configuration. Ou…
The minimum degree question for the Maker Breaker Domination Game
Jakob Führer, Georg Grasegger, Paul Hametner +1
The Maker Breaker Domination Game is a two player game played on a graph in which the players take turns to claim a vertex from the graph. The aim of the Dominator is to claim…
Convexity, Elementary Methods, and Distances
Oliver Roche-Newton, Dmitrii Zhelezov
This paper considers an extremal version of the Erdős distinct distances problem. For a point set , let denote the set of all Euclidean distances dete…
Large Convex sets in Difference sets
Krishnendu Bhowmick, Ben Lund, Oliver Roche-Newton
We give a construction of a convex set with cardinality such that contains a convex subset with cardinality . We also consider the following…
Local Differences Determined by Convex sets
Krishnendu Bhowmick, Miriam Patry, Oliver Roche-Newton
This paper introduces a new problem concerning additive properties of convex sets. Let be a set of real numbers and let $D_i(S)= \{s_x-s_y: 1 \leq x-y \l…
A better than exponent for iterated sums and products over
Oliver Roche-Newton
In this paper, we prove that the bound \[ \max \{ |8A-7A|,|5f(A)-4f(A)| \} \gg |A|^{\frac{3}{2} + \frac{1}{54}-o(1)} \] holds for all , and for all convex func…
Counting arcs in
Krishnendu Bhowmick, Oliver Roche-Newton
An arc in is a set such that no three points of are collinear. We use the method of hypergraph containers to prove several counting re…
A convex set with a rich difference
Oliver Roche-Newton, Audie Warren
We construct a convex set with cardinality and with the property that an element of the difference set can be represented in different ways. We also show that th…
Convexity, Squeezing, and the Elekes-Szabó Theorem
Oliver Roche-Newton, Elaine Wong
This paper explores the relationship between convexity and sum sets. In particular, we show that elementary number theoretical methods, principally the application of a squeezing p…
Convexity, Superquadratic Growth, and Dot Products
Brandon Hanson, Oliver Roche-Newton, Steven Senger
Let be a point set with cardinality . We give an improved bound for the number of dot products determined by , proving that, \[ |\{ p \cdot q :p,q \in…
Additive and multiplicative Sidon sets
Oliver Roche-Newton, Audie Warren
We give a construction of a set such that any subset with is neither an additive nor multiplicative Sidon set. In doing so…
The Elekes-Szabó Problem and the Uniformity Conjecture
Mehdi Makhul, Oliver Roche-Newton, Sophie Stevens +1
In this paper we give a conditional improvement to the Elekes-Szabó problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}…
Sums, products and dilates on sparse graphs
Oliver Roche-Newton
Let and . We prove that, for any , \[ \max \{|A+_G A|, |A+_G λA|, |A\cdot_G A|\} \gg |G|^{6/11}. \]
Higher convexity and iterated sum sets
Brandon Hanson, Oliver Roche-Newton, Misha Rudnev
Let be a smooth real function with strictly monotone first derivatives. We show that for a finite set , with , $|2^kf(A)-(2^k-1)f(A)|\gg_k |A|^{k+1-o(1)}…
Arcs in
Oliver Roche-Newton, Audie Warren
An arc is a subset of which does not contain any collinear triples. Let denote the number of arcs in with cardinality . This paper is pr…
An Energy Bound in the Affine Group
Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev +1
We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the a…
New Expander Bounds from Affine Group Energy
Oliver Roche-Newton, Audie Warren
The purpose of this article is to further explore how the structure of the affine group can be used to deduce new incidence theorems, and to explore sum-product type applications o…
Four-term progression free sets with three-term progressions in all large subsets
Cosmin Pohoata, Oliver Roche-Newton
This paper is mainly concerned with sets which do not contain four-term arithmetic progressions, but are still very rich in three term arithmetic progressions, in the sense that al…
Constructions for the Elekes-Szabó and Elekes-Rónyai problems
Mehdi Makhul, Oliver Roche-Newton, Audie Warren +1
We give a construction of a non-degenerate polynomial and a set of cardinality such that $\left|Z(F)\cap (A \times A \times A) \right| \gg n^{\frac{…
An improved bound for the size of the set
Oliver Roche-Newton
It is established that for any finite set of positive real numbers , we have
If is small then is superquadratic
Oliver Roche-Newton, Ilya D. Shkredov
This note proves that there exists positive constants and such that for all finite with we have .
On iterated product sets with shifts II
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
The main result of this paper is the following: for all there exists such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \s…
Improved Bounds for Pencils of Lines
Oliver Roche-Newton, Audie Warren
We consider a question raised by Rudnev: given four pencils of concurrent lines in , with the four centres of the pencils non-collinear, what is the maximum possib…