# 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.

**4**

**0**answers

### The original proof of Szemerédi's Theorem

**6**

**1**answer

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

**3**

**1**answer

### Freiman-isomorphic sets

**4**

**1**answer

### Reference to a variant of Abel's summation formula

**2**

**1**answer

### l-wise t-intersecting families of shifts of finite sets of integers

**3**

**2**answers

### Partition regular systems: do they have solution in (very dense) set of integers?

**1**

**1**answer

### Some divisibility constraints in Frobenius coin problem

**2**

**1**answer

### Intersections of translates of finite sets of integers

**3**

**1**answer

### Problem related to Frobenius coin problem

**1**

**0**answers

### Consecutive integers divisible by consecutive small numbers

**5**

**0**answers

### Some questions about the Lévy monoid of certain densities

**3**

**1**answer

### Exact statistics in the Frobenius coin problem

**9**

**0**answers

### An abstract zero-sum problem

**12**

**1**answer

### Where did the term “additive energy” originate?

**9**

**0**answers

### A characterization of quadratics similar to an inverse sieve problem

**9**

**0**answers

### Partition regularity in the squares

**7**

**1**answer

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

**7**

**1**answer

### Subsets of [1..N] with no three-term arithmetic progressions and no large gaps

**6**

**2**answers

### Additive energy of Piatetski-Shapiro sequences

**1**

**1**answer

### limit and combinatorics

**2**

**0**answers

### Additive combinatorics and a Diophantine equation

**14**

**1**answer

### Erdös-Turán via Hardy-Littlewood circle method?

**3**

**2**answers

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

**6**

**1**answer

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

**3**

**0**answers

### Area defined with $\pm$ closedness

**23**

**0**answers

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

**6**

**1**answer

### What pairs of sets have additive energy?

**2**

**1**answer

### Elaboration of a certain section of a paper by Thanigasalam

**6**

**2**answers

### Determining when combinatorial sums are zero

**2**

**1**answer

### On the upper Banach density of the set of positive integers whose base-$b$ representation misses at least one prescribed digit

**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?

**7**

**0**answers

### Distribution of trivial subset sums

**3**

**0**answers

### Goldbach's problem in algebraic number fields [duplicate]

**3**

**1**answer

### When are the powers of 2 sum-free mod n?

**3**

**1**answer

### higher dimensional analogue of EGZ theorem

**5**

**1**answer

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

**2**

**0**answers

### Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?

**4**

**1**answer

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

**2**

**1**answer

### Representation numbers of numerical semigroups

**4**

**1**answer

### Approximate homomorphisms

**3**

**2**answers

### Who needs a symmetric upper asymptotic density on the integers?

**4**

**0**answers

### Sparsifiers for 3-term arithmetic progressions

**10**

**2**answers

### Iterated sumset inequalities in cancellative semigroups

**1**

**1**answer

### Ask the name of a combinatorial theorem

**10**

**2**answers

### Sumsets and dilates: does $|A+\lambda A|<|A+A|$ ever hold?

**3**

**0**answers

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

**7**

**2**answers

### What methods do we have to understand the spectrum of matrices with restricted entries?

**0**

**1**answer

### What is the maximal number of solutions of $\sum_{i = 1}^n 1/a_i^x - \sum_{i = 1}^m 1/b_i^x = 0$?

**23**

**1**answer

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

**2**

**0**answers