Arithmetic combinatorics

Known as: Additive combinatorics, Multiplicative combinatorics

In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.

Papers overview

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2018

I would like to thank Trinity College and Department of Pure Mathematics and Mathematical Statistics for their generous…

2017

We consider the problem of identity testing of two "hidden" monic polynomials $f$ and $g$, given an oracle access to $f(x)^e$ and…

2017

We adapt the idea of higher moment energies, originally used in Additive Combinatorics, so that it would apply to problems in…

2016

Author(s): Tait, Michael | Advisor(s): Verstraete, Jacques | Abstract: This thesis studies problems in extremal graph theory…

2015

Let $\mathcal{P}$ be a probability distribution over a finite alphabet $\Omega^\ell$ with all $\ell$ marginals equal. Let…

2015

Over the past few years, a family of interesting new inequali ties for the entropies of sums and differences of random variables…

2013

We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open…

2010

We generalize Burgess' results on partial Gaussian sums to arbitrary finite fields. The main ingredients are the classical method…

2008

In a recent paper \cite{Gl} A. Glibichuk proved that if $A,B$ are subsets of an arbitrary finite filed $\F_q$, such that $|A||B…

2007

E-thesis pagination differs from approved hard bound copy, Cambridge University Library classmark: PhD.30726