T. Sanders

activity

20062026

most citedOn the Bogolyubov-Ruzsa lemma

157 citations · 642 across the 35 of their papers we have counts for

collaborators

Showing 2018Show all

6 papers · 1 filter

math.CO2018

The stability of finite sets in dyadic groups

Tom Sanders

We show that there is an absolute $c > 0$ such that any subset of $F_{2}^{\infty}$ of size $N$ is $O (N^{1 - c})$ -stable in the sense of Terry and Wolf. By contrast a size $N$ arit…

math.CO2018

The coset and stability rings

Tom Sanders

We show that if $G$ is a discrete Abelian group and $A \subset G$ has $∥ 1_{A} ∥_{B (G)} \leq M$ then $A$ is $O (exp (π M))$ -stable in the sense of Terry and Wolf.

math.CO2018

Almost homomorphisms between the Boolean cube and groups of prime order

Tom Sanders

We show that if f is an injection from an n-dimensional Boolean cube (considered as an additive group) to a group of prime order then the probability that f(x+y)=f(x)+f(y) is O(2^{…

math.CA2018

Coset decision trees and the Fourier algebra

Tom Sanders

We show that if G is a finite group and f is a {0,1}-valued function on G with Fourier algebra norm at most M then f may be computed by a coset decision tree (that is a decision tr…

math.CA2018★ 5 cited

Boolean functions with small spectral norm, revisited

Tom Sanders

We show that if $f$ is an integer-valued function with spectral norm at most $M$ then there are subspaces $V_{1}, \dots, V_{L}$ and signs $σ_{1}, \dots, σ_{L} \in {- 1, 1}$ such that $f=σ_1 1_…

math.CA2018

The Erdos-Moser sum-free set problem

Tom Sanders

We show that if A is a finite set of integers then it has a subset S of size \log^{1+c} |A| (c>0 absolute) such that s+s' is never in A when s and s' are distinct elements of S.