# 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.

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

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### An extremal combinatorics problem

**5**

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### Convex subsets of sumsets

**3**

**1**answer

### Lower bound for k-fold Sidon Sets

**2**

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

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

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

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### Which sets of roots of unity give a polynomial with nonnegative coefficients?

**1**

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

**3**

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### Inequalities about tripling and doubling sumsets

**3**

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### A new combinatorial problem for finite groups

**2**

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

**12**

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### Factorizable groups

**7**

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### Cyclic and prime factorizations of finite groups

**10**

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### Is each finite group multifactorizable?

**-1**

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### Discrepancy in non-homogeneous arithmetic progressions

**3**

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

**6**

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

**4**

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

**1**

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

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**2**answers

### Analytical result of a combination like generating function

**6**

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

**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

**20**

**2**answers

### EGZ theorem (Erdős-Ginzburg-Ziv)

**6**

**1**answer

### A combinatorial property of uncountable groups

**8**

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### Distribution of subset-sums

**3**

**1**answer

### On decomposition of finite Abelian groups

**3**

**1**answer

### Sidon Sets and Diophantine Equation

**3**

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

**12**

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### Escaping from a centralizer

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### Polynomials passing through points with tangential conditions

**1**

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### Equivalent condition for Poincare polynomial

**4**

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

**6**

**1**answer

### The soccer splitting problem in arbitrary commutative ring

**0**

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### Infinite difference length of integer subsets

**5**

**2**answers

### The number of co-circular four tuples

**5**

**1**answer

### Additive basis of order 2

**4**

**1**answer

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

**2**

**2**answers

### asymptotic for restricted partitions

**1**

**1**answer

### Some divisibility constraints in Frobenius coin problem

**6**

**1**answer

### A permutation problem

**3**

**1**answer

### Density version of the Erdos-Graham conjecture

**7**

**1**answer

### Is $AA+A$ always at least as large as $A/A$?

**3**

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

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### Maximum-size sum sets

**4**

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### Balancing points with lines

**7**

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

**5**

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

**3**

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