# 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.

**3**

**1**answer

### A variance computation

**4**

**1**answer

### Which cyclic groups admit a difference set?

**3**

**1**answer

### Large gaps in Singer planar difference sets?

**11**

**1**answer

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

**15**

**4**answers

### Are all partial consecutive harmonic subsums distinct?

**3**

**0**answers

### Given a primitive finite set $A\subseteq\bf N$ with $0\in A$, find two more primitive sets $B,C\subseteq\bf N$ with $B\ne C$ and $A+B=A+C$

**4**

**0**answers

### Two variants of the Littlewood-Offord theorem

**2**

**0**answers

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

**1**

**1**answer

### Covering a finite ring with arithmetic progressions

**1**

**0**answers

### maximum subsets of a certain type contained in difference set

**2**

**2**answers

### Playing leapfrog with primes

**3**

**3**answers

### Computation of a series

**0**

**1**answer

### Sets with $\mathrm{d}(h\mathscr{A}) = 1$ but s.t. $h\mathscr{A}$ doesn't contain all large integers

**3**

**0**answers

### Probabilistic proof for “regularity”

**4**

**2**answers

### How big must the sumset $A+A$ be if $A$ satisfies no translation-invariant equations of low height?

**2**

**1**answer

### What if $|A+A|$ is proportional to $|A|^{1 + \delta}$?

**2**

**0**answers

### Partitioning an interval into subsum-free sets

**3**

**2**answers

### Two equivalent statements about primes

**6**

**2**answers

### Gromov's pseudogroups and Tao's approximate groups

**1**

**0**answers

### Growth of products of large sets in Lie groups

**3**

**2**answers

### No Sidon sequence which is an asymptotic basis of order $2$

**3**

**0**answers

### Strong criteria for additive non-basis

**4**

**0**answers

### An inequality from Green-Tao “The primes contain arbitrary long arithmetic progressions”

**12**

**1**answer

### Is there a strictly increasing sequence such that it is o(2^n) and any term cannot equal the sum of any unrepeated predecessors?

**1**

**0**answers

### Are the Beatty primes asymptotically (Gowers) uniform?

**4**

**0**answers

### Negative values of cosine sums

**1**

**1**answer

### Invariant complementary sets modulo $p$

**0**

**1**answer

### Geometric progression modulo p [closed]

**3**

**1**answer

### (Extremal) arithmetic combinatorics in non-abelian groups

**3**

**0**answers

### Number of classes $\pmod p$ represented by $b_1s^{n-1} + \dots + b_n$ where $ord_p(s) = n$

**11**

**2**answers

### Small set such that $\{1 , \ldots , n\} \cdot A = \mathbb{Z} / p \mathbb{Z}$

**0**

**1**answer

### Is budget-additive function a modular set function?

**1**

**1**answer

### Approximation of sets

**0**

**1**answer

### On Sylvester's coin problem for geometric progressions

**8**

**0**answers

### What is intuition behind sets with more sums than differences?

**4**

**0**answers

### Restricted addition analogue of Freiman's $(3n-4)$-theorem

**2**

**1**answer

### When does the equality hold in Dias da Silva - Hamidoune Theorem?

**0**

**1**answer

### Sumset achieving extreme upper bound [closed]

**3**

**1**answer

### Lower bound construction for Multidimensional Szemerédi's Theorem

**6**

**1**answer

### Is the exponent $2$ sharp in the Balog-Szemerédi-Gowers Theorem?

**15**

**1**answer

### Combinatorics problem about sum of natural numbers

**4**

**1**answer

### Find a subset such that its sum is divisible by $n$

**8**

**0**answers

### Sets of natural numbers which are almost closed under addition

**0**

**0**answers

### Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$

**3**

**1**answer

### Does positive relative density imply asymptotic additive basis behaviour?

**8**

**1**answer

### Largeness and arithmetic progression properties of generic reals

**6**

**1**answer

### Zero-sum sets in union-closed families

**3**

**1**answer

### 3-dimensional vectors satisfying certain equalities

**14**

**3**answers

### A seemingly simple combinatorial object that must have an easy generating function

**7**

**1**answer