# 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.

**1**

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### Almost quadratic difference sets

**-1**

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### A number related to rank

**2**

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### On norms of Boolean functions

**6**

**1**answer

### Maximum size of $k$-Sidon set over $\mathbb{F}_2^n.$

**2**

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### Sumset of $k$-smooth numbers

**5**

**1**answer

### Computational version of inverse sumset question

**1**

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### Bell polynomial with variables 1 and 0

**3**

**1**answer

### Unique representation and sumsets

**-2**

**1**answer

### What are the consequence of Snevily's conjecture to analytic number theory if really there is a connection between them? [closed]

**1**

**1**answer

### Average size of iterated sumset modulo $p-1$,

**1**

**1**answer

### Does $g+A\subseteq A+A$ imply $g\in A$?

**9**

**3**answers

### Does the expression $x^4 +y^4$ take on all values in $\mathbb{Z}/p\mathbb{Z}$?

**7**

**1**answer

### Finite concatenation-free languages

**2**

**1**answer

### Well-spread (weak Sidon) sets

**3**

**1**answer

### Asymptotic number of $3$-AP's in a set $A\subseteq\mathbb{F}_{p}^{n}$ of density $\epsilon$

**3**

**1**answer

### Why should it be hard to generalize Dvir's proof of the finite field Kakeya conjecture to the Euclidean case?

**2**

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### Does there exist a subset $E \in \mathbb{Z}_{p^2}^4$ such that $\Pi(E) \neq \mathbb{Z}_p$?

**1**

**1**answer

### Find the largest subset of all binary arrays of length $n$ with $r$ ones which have pairwise distance greater than $m$

**5**

**4**answers

### Request for an exact formula related to a partition in number theory

**1**

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### Packing almost-subgroups into a group

**1**

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### Sidon sets in finite groups

**1**

**1**answer

### What is the minimal possible size of a subset of this semigroup satisfying the following conditions?

**0**

**1**answer

### Set of numbers with unique results from sums [closed]

**7**

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### Corners theorem in finite fields

**4**

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### A conjecture on the cardinality of minimal mediated sequences

**3**

**1**answer

### weak piecewise syndetic property for positive upper banach density set

**9**

**1**answer

### Sidon sets of $\mathbb{Z}/p\mathbb{Z}$

**0**

**0**answers

### A gap problem in elementary additive combinatorics

**5**

**2**answers

### Nontrivial expansion in sumsets

**1**

**1**answer

### Results on additive structure of polynomial rings?

**6**

**1**answer

### Sum of two $n$-th powers, of two $m$-th powers, but not of two $mn$-th powers

**10**

**1**answer

### Freiman inequality for projective space?

**2**

**1**answer

### Chain of sequences, such that $a_{k+1}(n)$ completes $a_k(n)$

**15**

**3**answers

### Size of sets with complete double

**1**

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### Is every positive-density set of positive integers almost rational?

**5**

**1**answer

### Maximum size of a critical set that sums to $n$

**6**

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### When is $\{s_2-s_1,s_3-s_2,s_1-s_3\}\cap S$ non-empty for any $s_1,s_2,s_3\in S$?

**3**

**1**answer

### Sum-product estimate in finite fields

**0**

**0**answers

### Number of nontrivial solutions to equations of given genus (Ruzsa)

**5**

**1**answer

### Eccentricity in the number of representations for sets too large to be Sidon sets

**3**

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### Under what conditions on $A$ and $v$ is the size of the sumset $v \cdot A + A$ over $\mathbb{F}_p$ equal or close to $|A|^2$?

**5**

**2**answers

### $|(A+B)(X)|=o(X)$ if $|A(X)|=O(X^{1/2})$ and $|B(X)|=O(X^{1/2})$?

**0**

**0**answers

### On bounds for $|A+\operatorname{rad}(A)|$, where $A$ is a finite set of positive integers

**1**

**1**answer

### Representing natural numbers as sums of powers of distinct numbers

**5**

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### Low-rank approximation over finite fields

**9**

**2**answers

### Sets A such that A+A contains the largest set [0,1,..,t]

**3**

**0**answers

### A question on a result of Imre Ruzsa concerning sum-sets

**10**

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### Bijections $\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}$ with vanishing local means

**5**

**0**answers

### What is the “right” notion of exponentiation in $\beta \mathbb N$?

**7**

**0**answers