# 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.

**100**

**7**answers

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

**3**

**0**answers

### On covering by smooth numbers

**5**

**2**answers

### Ordered lattice point enumeration

**5**

**1**answer

### Element with unique representation in A+B

**4**

**4**answers

### Applications of Szemeredi's Theorem

**2**

**0**answers

### How is the structure of spectrum in cap-sets with no strong increments unrealistic if density is too large?

**2**

**1**answer

### On a problem about $GF(2)^n$

**5**

**3**answers

### Sets of natural numbers with finite intersections and divergent sums of reciprocals

**3**

**0**answers

### Applications of Freiman's theorem?

**1**

**1**answer

### Pollard's inequality modulo a composite number

**2**

**1**answer

### Proof of Pollard's inequality

**11**

**2**answers

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

**3**

**0**answers

### Solving a doubly exponential generating function

**3**

**1**answer

### Packing bounds for sumsets, or, very discrete balls

**3**

**2**answers

### Number of subsum of a given set of integers

**7**

**3**answers

### Polynomial expressions of roots of unity with integer norm

**13**

**0**answers

### How large must $A$ be if $\{1, \ldots, N\} \subseteq A-A$?

**2**

**2**answers

### asymptotic for restricted partitions

**2**

**2**answers

### Functions representable as a sum of two permutations of Z/nZ

**3**

**1**answer

### How to generate $n$ FP32 rationals s.t. no two distinct k-el. subsets have same sum?

**14**

**1**answer

### Minimal “sumset basis” in the discrete linear space $\mathbb F_2^n$

**2**

**0**answers

### Sets of coprime numbers

**4**

**0**answers

### Reduction argument from a general vertex set V(G) to a prime power in Prof. Keevash's proof on the Existence of Designs

**2**

**1**answer

### every arithmetic progression contains a sequence of $k$ “consecutive” primes for possibly all natural numbers $k$?

**5**

**0**answers

### The sum of all the elements of every non empty subset of $A$ is not a multiple of $n$

**0**

**0**answers

### Integral representation of the function

**1**

**1**answer

### Finding a sufficiently large complete bipartite subgraph using matrix counting

**7**

**0**answers

### Why have most maximal cliques of Paley graphs odd size?

**1**

**1**answer

### Expression and growth bound for $r_{p^m,k}(n)$

**0**

**1**answer

### Monotonicity of the gap of permutated sequence

**2**

**1**answer

### Growth of $r_k(n)$

**4**

**0**answers

### Subgroup cliques in the Paley graph

**2**

**2**answers

### Asymptotic formula for the number of ways to write a number as the sum of $k$ triangular numbers

**1**

**1**answer

### Subset of the integers with certain properties

**1**

**0**answers

### $B_k[1]$ sets with smallest possible $m = max B_k[1]$ for given $k$ and $n = |B_k[1]|$ elements

**4**

**1**answer

### Spectrum of image of a Freiman Homomorphism

**5**

**2**answers

### Intuition for Freiman dimension

**23**

**1**answer

### integers which are sums of binomial coefficients: $\sum_i {n \choose k_i}$

**2**

**0**answers

### Can the affine sieve be used to sieve for $k$-free values?

**15**

**1**answer

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

**5**

**2**answers

### Size of distinct sums in A

**8**

**0**answers

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

**10**

**3**answers

### Examples of specializations of elementary symmetric polynomials

**6**

**5**answers

### What makes a set random?

**10**

**2**answers

### Large sets $X \subseteq \mathbb{Z}_2^n$ with $X+X \ne \mathbb{Z}_2^n$

**3**

**0**answers

### Sets of polynomials with restricted set of products

**25**

**3**answers

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

**-1**

**1**answer

### Collecting terms of a linear expression with nested sums and combinatorics in coefficients

**4**

**1**answer

### Circle method on things other than the integers

**0**

**0**answers