# 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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### For any $n-1$ elements of $\mathbb Z/n\mathbb Z$, we can make $0$ using $\{-,+,\times\}$ without parentheses

**3**

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### Difference set of difference set

**5**

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### Does any subset of a finitely generated group with positive upper density contain three points in arithmetic progression?

**7**

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### When does $A-A$ avoid $A$?

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### Reference request: Efficient representations of lattice elements as sums of generators

**1**

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### Expectation of the sum of the squares of the cardinal of an inverse function

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### Is there a permutation $\tau\in S_n$ with $\tau(1)^{\tau(2)}+\cdots+\tau(n-1)^{\tau(n)}+\tau(n)^{\tau(1)}$ a square?

**14**

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### Exact coverability of $\mathbb{Z}_n$ by cyclic shifts of a given set — easy? NP-complete?

**3**

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### Ramsey Numbers for Integers

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### Strengthening of Freiman's theorem

**1**

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### Complexity of checking if a set is an additive basis

**0**

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### Lower Bound on Structured Fourier Coefficients

**48**

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### Is each squared finite group trivial?

**7**

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### Bounding size of partial difference sets given size of partial sumsets

**1**

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### Converse to Hausdorff-Young (or Riesz-Thorin) for finite cyclic groups?

**0**

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### Norms of ideals in number fields as additive bases

**6**

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### Primitive recursive bounds for the the Gallai-Witt theorem

**7**

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### Arithmetic progressions in inverse image of totient function

**4**

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### A combinatorial problem on abelian groups

**18**

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### Characterizing the elements of $(A-A)/(A-A)$, where $A$ is a Cantor-like subset of the integers

**8**

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### Maximum density of a set without a fixed pattern

**1**

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### Counting solutions of a equation involving prime powers

**10**

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### Converse to Erdős' conjecture on arithmetic progressions

**6**

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### Analogue to Szemerédi's theorem for non-monotone sequences

**5**

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### Is there a short proof for the permutation invariance of this combinatorial map?

**1**

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### $\ell^1$-bound on graph laplacian with weight

**2**

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### What is the importance of “small doubling” in the theory of approximate groups?

**3**

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### Ellenberg and Gijswijt's result on arithmetic progressions in subsets of $\mathbb{F}_q^n$ and a generalisation to sets of linear equations

**7**

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### Sets of residues with only a single intersection under translation

**0**

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### Distributions associated with random sets and sums of random sets

**6**

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### Is there any relationship between Szemerédi's theorem and Sunflower conjecture?

**2**

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### Origins of the ``baby Freiman'' theorem

**3**

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### Prime gap distribution in residue classes and Goldbach-type conjectures

**11**

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### A problem in additive combinatorics

**1**

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### Congruential equidistribution, prime numbers, and Goldbach conjecture

**1**

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### Curious inversion formula in additive combinatorics

**0**

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### Paradox in additive combinatorics

**0**

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### General asymptotic result in additive combinatorics (sums of sets)

**7**

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### A conjecture on circular permutations of n elements in an abelian group of odd order

**5**

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### Goldbach conjecture and other problems in additive combinatorics

**5**

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### Is every integer $\ge 312$ the sum of two integers with triangular divisors?

**5**

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### A variant of the capset problem

**3**

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### Almost quadratic difference sets

**2**

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### On norms of Boolean functions

**6**

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### Maximum size of $k$-Sidon set over $\mathbb{F}_2^n.$

**2**

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### Sumset of $k$-smooth numbers

**5**

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### Computational version of inverse sumset question

**1**

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### Bell polynomial with variables 1 and 0

**3**

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### Unique representation and sumsets

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