# 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.

**45**

**3**answers

### Number of elements in the set $\{1,\cdots,n\}\cdot\{1,\cdots,n\}$

**7**

**1**answer

### Difference Sets

**33**

**4**answers

### Cliques, Paley graphs and quadratic residues

**23**

**1**answer

### Two conjectures about zero inner products and dissociated sets

**6**

**1**answer

### Additivity of upper densities with respect to arithmetic progressions of integers

**18**

**3**answers

### The sum of integers being a bijection

**3**

**0**answers

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

**3**

**0**answers

### Reference for a lemma on the asymptotic upper density of special sets with large gaps and intervals

**100**

**7**answers

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

**19**

**4**answers

### Number of vectors so that no two subset sums are equal

**24**

**2**answers

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

**23**

**3**answers

### How many different numbers can be obtained as product of first $n$ natural numbers?

**9**

**1**answer

### Who was/were the first to note that if $\sum_{x \in X} \frac{1}{x} < \infty$ then the natural density of $X$ is zero?

**10**

**3**answers

### Is each finite group multifactorizable?

**4**

**1**answer

### Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property

**4**

**2**answers

### Anticoncentration of the convolution of two characteristic functions

**3**

**1**answer

### Is every sufficiently dense well mixed set an additive basis?

**1**

**1**answer

### Covering a finite ring with arithmetic progressions

**46**

**5**answers

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

**14**

**1**answer

### On the $L^1$-norm of certain exponential sums.

**25**

**3**answers

### Ordering subsets of the cyclic group to give distinct partial sums

**26**

**3**answers

### long enough interval of integers to solve a simultaneous congruence

**23**

**0**answers

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

**7**

**2**answers

### Recent results on the Gauss circle problem?

**22**

**1**answer

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

**26**

**2**answers

### The Erdős-Turán conjecture or the Erdős' conjecture?

**12**

**2**answers

### Factorizable groups

**15**

**1**answer

### Sum and product estimate over integers, rationals, and reals

**12**

**2**answers

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

**9**

**0**answers

### An abstract zero-sum problem

**6**

**1**answer

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

**14**

**1**answer

### What is the smallest cardinality of a self-linked set in a finite cyclic group?

**11**

**2**answers

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

**9**

**4**answers

### Binomial coefficient in Andrews' partition book

**13**

**1**answer

### Near-linear mappings from $\mathbb F_p$ to $\mathbb R$

**11**

**2**answers

### Most dense subset of numbers that avoids arbitrarily long arithmetic progressions

**7**

**0**answers

### Distribution of trivial subset sums

**6**

**0**answers

### Small maximal sets with no 3-AP?

**5**

**1**answer

### Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$

**3**

**1**answer

### Bounding the size of certain sumsets in the plane

**3**

**2**answers

### Is the sumset or the sumset of the square set always large?

**3**

**2**answers

### Two equivalent statements about primes

**2**

**1**answer

### Karolyi's theorem for finite groups and its extensions

**2**

**0**answers

### A set in Z/nZ which contains two elements, one of which is a small multiple of the other

**11**

**1**answer

### What is the smallest cardinality of a set A whose difference A-A contains $n$ consequtive integer numbers?

**8**

**0**answers

### A strong sum-product “for translates” in finite fields

**6**

**1**answer

### Are the extremal points of a certain set of functions $\mathcal P(\mathbf N) \to \bf R$ weakly additive?

**5**

**1**answer

### Divisibility labeling on a boolean lattice and nonzero Euler totient

**4**

**1**answer

### Set of small numbers with distinct $k$-sums

**3**

**1**answer