# Questions tagged [additive-combinatorics]

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.

**19**

**3**answers

### Can nonabelian groups be detected “locally”?

**7**

**1**answer

### Minimum cardinality of a difference set in $R^n$

**18**

**3**answers

### An “Average” Erdős–Turán conjecture

**3**

**1**answer

### Optimize / simple Set Covering Problem

**2**

**3**answers

### Arithmetic progressions of length 3 in subset of Z_n of size n^d

**2**

**0**answers

### Prime divisors of the difference set

**4**

**1**answer

### Size of Sum Sets

**7**

**1**answer

### Fourier analysis, orthogonality, and Plancherel for finite abelian groups

**6**

**0**answers

### Expectation of Gowers norm

**16**

**2**answers

### Roth's theorem and Behrend's lower bound

**5**

**3**answers

### Structure of nonaveraging sets of integers

**20**

**4**answers

### Arithmetic progressions inside polynomial sets

**2**

**0**answers

### Fun question in additive combinatorics

**6**

**1**answer

### Bounds on the size of sets not containing a given finite pattern

**24**

**2**answers

### Partitions to different parts not exceeding $n$

**5**

**1**answer

### Thin subbases for the primes?

**4**

**1**answer

### Methods to determine whether a given set is the sum of other sets

**3**

**2**answers

### Choice of normalization of the finite Fourier transform

**1**

**1**answer

### In what cases are the counting function and representation functions strongly related?

**6**

**2**answers

### Known additive bases with irregular counting function

**5**

**1**answer

### How large can a non-sumset be?

**14**

**3**answers

### When does $P(a−b)=0$ for $a≠b$ ensure $P(0)=0$? (Continued.)

**12**

**2**answers

### Arithmetic progressions modulo $p$ under the squaring map

**9**

**1**answer

### When does $P(a-b)=0$ for $a\ne b$ ensure $P(0)=0$?

**5**

**3**answers

### Any rigorous way to claim that sums with repeat summands are few?

**7**

**2**answers

### Recent results on the Gauss circle problem?

**4**

**0**answers

### A question about Erdos thin bases

**11**

**2**answers

### Sums of subsets of $\mathbb{Z}/n\mathbb{Z}$

**6**

**1**answer

### Arbitrarily thin additive bases of the natural numbers

**5**

**1**answer

### A question on the singular series and singular integral in Hardy-Littlewood Circle Method

**18**

**3**answers

### The sum of integers being a bijection

**6**

**2**answers

### Inverse Length 3 Arithmetic Progression Problem for sets with positive upper density

**12**

**2**answers

### Did Erdős publish his proof of the multiplicative version of the Erdős-Turán conjecture?

**4**

**1**answer

### Is the generalized Erdős–Heilbronn problem true for finite cyclic groups?

**1**

**2**answers

### Almost periodic functions in Tao's ergodic proof of Szemerédi's theorem

**33**

**4**answers

### Cliques, Paley graphs and quadratic residues

**16**

**3**answers

### What is the shortest route to Roth's theorem?

**6**

**1**answer

### Upper bound for size of subsets of a finite group that contains a sum-full set

**11**

**7**answers

### describe subsets of the integers closed under the binary operation Ax+By

**3**

**1**answer

### Queries about the Skolem-Mahler-Lech theorem (integer zeros of exponential polynomials)

**7**

**1**answer

### Homogeneous arithmetic progressions in difference sets

**5**

**1**answer

### Cauchy-Davenport strengthening?

**6**

**1**answer

### Additive combinatorics and large Fourier coefficients

**4**

**2**answers

### Sum of sets modulo a square

**22**

**1**answer

### Monochromatic triangles in every two-coloring of the plane?

**7**

**1**answer

### A variation of Minkowski sum

**2**

**3**answers

### Given N points on a number line and m total distances between those points, are there efficent ways to optimize for particular values in m?

**20**

**2**answers

### EGZ theorem (Erdős-Ginzburg-Ziv)

**15**

**1**answer

### Goldbach-type theorems from dense models?

**5**

**2**answers