# 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.

**0**

**0**answers

### Number of $b$-separated Sidon sets with pairwise difference set intersection bounds

**4**

**2**answers

### An extremal combinatorics problem

**2**

**0**answers

### On an exercise in The Probabilistic Method : random dilate of a set in a finite field

**46**

**5**answers

### Jean Bourgain's Relatively Lesser Known Significant Contributions

**11**

**2**answers

### Maximize $f(0)+\cdots+f(n-1)$ subject to $f(x)f(y) + f(x+y) \leq 1$

**1**

**1**answer

### Largest cardinality $n$ of a subset $A$ of $\{1,2,\ldots,M\}$ such that $(A+A) \cap A$ is empty

**3**

**0**answers

### Inequalities about tripling and doubling sumsets

**3**

**0**answers

### A new combinatorial problem for finite groups

**7**

**0**answers

### Cyclic and prime factorizations of finite groups

**-1**

**1**answer

### Discrepancy in non-homogeneous arithmetic progressions

**10**

**3**answers

### Is each finite group multifactorizable?

**12**

**2**answers

### Factorizable groups

**2**

**0**answers

### On the set $\{\sum_{k=1}^n \lambda_ka_k:\ a_1,\ldots,a_k\ \text{are distinct elements of}\ A\}$

**3**

**0**answers

### A conjectural lower bound for $|\{\sum_{k=1}^nka_k:\ a_1,\ldots,a_n\ \text{are distinct elements of }\ A\}|$

**6**

**0**answers

### Sets $X,Y$ of natural numbers such that any natural $n$ writes uniquely $n=x+y$ [duplicate]

**4**

**0**answers

### Lower bound for some sums of roots of unity

**1**

**0**answers

### Has anyone studied Golomb rulers having a spectrum with a minimal $L^2$ norm?

**0**

**2**answers

### Analytical result of a combination like generating function

**6**

**0**answers

### Legendre's three-square theorem and squared norm of integer matrices

**3**

**1**answer

### Lower bound for k-fold Sidon Sets

**11**

**2**answers

### Extension of Dickson's theorem on integers of the form $a^2+b^2+2c^2$

**34**

**3**answers

### Lagrange four squares theorem

**6**

**1**answer

### A combinatorial property of uncountable groups

**3**

**1**answer

### On decomposition of finite Abelian groups

**3**

**1**answer

### Sidon Sets and Diophantine Equation

**3**

**0**answers

### A Freiman-type of question for sets with small doubling costant

**12**

**0**answers

### Escaping from a centralizer

**2**

**0**answers

### Polynomials passing through points with tangential conditions

**1**

**0**answers

### Equivalent condition for Poincare polynomial

**0**

**0**answers

### Infinite difference length of integer subsets

**6**

**1**answer

### The soccer splitting problem in arbitrary commutative ring

**5**

**2**answers

### The number of co-circular four tuples

**5**

**1**answer

### Additive basis of order 2

**3**

**1**answer

### Density version of the Erdos-Graham conjecture

**6**

**1**answer

### A permutation problem

**3**

**0**answers

### Does every $n\times n\times n$ Latin cube contain a Latin transversal?

**0**

**0**answers

### Maximum-size sum sets

**4**

**1**answer

### A permutation problem for finite subsets of an abelian group

**7**

**0**answers

### Is every integer $n>1$ the sum of two squares and two central binomial coefficients?

**4**

**1**answer

### Balancing points with lines

**5**

**0**answers

### Is every integer $n>1$ the sum of two triangular numbers and two powers of $5$?

**4**

**1**answer

### Asymptotic for number of partitions of $n$ into $k$ squares, uniform in $n,k \to +\infty$

**3**

**0**answers

### Decomposing a subset of $\mathbf Z$ into a sumset of irreducibles

**5**

**0**answers

### $m$-thick sets with small $n$-fold sumsets in finite cyclic groups

**15**

**3**answers

### Is there an “analytical” version of Tao's uncertainty principle?

**1**

**0**answers

### Prove A Skipping Prime Conjecture For Rio?

**1**

**1**answer

### Behrend's Construction

**1**

**1**answer

### Existence of Arithmetic Progression from density inequality

**4**

**1**answer

### Sets $A$ stable under $(x,f(x))\mapsto x+f(x)$

**0**

**0**answers