Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.

665 questions
Filter by
Sorted by
Tagged with
201 views

• 4,969
255 views

717 views

### Subsets of $(\mathbb{Z}/p)^{\times n}$

There seems to be some combinatorial fact that every subset $A$ of $G=(\mathbb{Z}/p)^{\times n}$ of cardinality $\frac{p^n-1}{p-1}+1$ containing $\vec{0}$ satisfies $(p-1)A=G$. ($p$ is a prime number....
• 153
1 vote
166 views

• 298
657 views

### A variant of the corners problem

Question: What is the size of the largest subset of $[n]^2$ containing no three point configurations of the form $(x,y), (x,y+d), (x+d,y')$ with $d \neq 0$? In particular, is it at most $O(n)$? Recall ...
• 530
170 views

### Equivalent formulation of Szemerédi-Trotter theorem

I am reading the first chapter of Adam Sheffer's book "Polynomial Methods and Incidence Theory" and in Lemma 1.15 he proves an equivalent formulation of Szemerédi-Trotter theorem. Before ...
• 298
409 views

• 3,403
214 views

### Bins-and-primes (prime divisors of $\prod(a_i-a_j)$, II)

This is a refined version of a question I have recently posted. For a prime $p$, let $\varphi_p\colon\mathbb Z\to\mathbb Z/p\mathbb Z$ denote the canonical homomorphism from the integers onto the ...
• 22.8k
156 views

### Prime divisors of $\prod(a_i-a_j)$

For a prime $p$, let $\varphi_p\colon\mathbb Z\to\mathbb Z/p\mathbb Z$ denote the canonical homomorphism from the integers onto the group of order $p$. Given an integer $n\ge 3$, what is the smallest ...
• 22.8k
42 views

Let $(G,+,0)$ be an abelian group, $H=(V,\mathcal{E})$ is a $r$-uniform hypergraph. Let $\ell:V\to G$ be a labelling of the vertices. The label of an edge is the sum of the label of the vertices, so $\... • 583 3 votes 0 answers 90 views ### Dimension of a kernel of a cocycle map Inspired by a previous question (Dimension of a kernel of a linear map) and some of the answers I was given I thought wheter I can generalize the question to the following: Compute the kernel (or at ... • 577 8 votes 1 answer 303 views ### The growth rate of a commutator set in a non-elementary group Let$G$be a non-elementary group generated by a finite set$S$. Here, a group is called non-elementary if it is not virtually abelian. Denote$S^{\le n}:=\{g\in G: |g|_S\le n\}$for any$n\in \mathbb ...
• 145
1 vote
For each positive integer $n$, let $q(n)$ denote the number of ways to write $n$ as a sum of distinct positive integers. We call those $q(n)\ (n=1,2,3,\ldots)$ strict partition numbers. The sequence \$...