# 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.

**23**

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

**23**

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### probability of zero subset sum

**13**

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

**13**

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### Correlation of Fourier transforms of characteristic functions

**12**

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### Escaping from a centralizer

**11**

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### What are the limits of the Erdős-Rankin method for covering intervals by arithmetic progressions?

**9**

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### An abstract zero-sum problem

**9**

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

**9**

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### Partition regularity in the squares

**9**

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### Cliques in the Paley graph and a problem of Sarkozy

**8**

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

**8**

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

**8**

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

**8**

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### Erdös-Fuchs Theorem for multivariate linear forms

**8**

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### Distribution of subset-sums

**7**

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### Cyclic and prime factorizations of finite groups

**7**

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### Is every integer $n>1$ the sum of two squares and two central binomial coefficients?

**7**

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### Distribution of trivial subset sums

**7**

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

**6**

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### Legendre's three-square theorem and squared norm of integer matrices

**6**

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### A formula for Frobenius number of certain numerical semigroups

**6**

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### Growth in a vector space

**6**

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### Large cubes in sum/difference sets

**6**

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### Other applications of the 'increment' approach

**6**

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### Largest set of integers without 3-term arithmetic progressions mod $n$

**6**

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

**6**

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### Expectation of Gowers norm

**5**

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### Is every integer $n>1$ the sum of two triangular numbers and two powers of $5$?

**5**

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### $m$-thick sets with small $n$-fold sumsets in finite cyclic groups

**5**

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### Increasing sequences in polynomial progressions modulo p

**5**

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

**5**

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

**4**

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### Lower bound for some sums of roots of unity

**4**

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### Linear combination of characters

**4**

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### On point sets with many distinct distances

**4**

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### Two variants of the Littlewood-Offord theorem

**4**

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

**4**

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### Negative values of cosine sums

**4**

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

**4**

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### The original proof of Szemerédi's Theorem

**4**

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### Sparsifiers for 3-term arithmetic progressions

**4**

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

**4**

**0**answers

### Subgroup cliques in the Paley graph

**4**

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### Distribution of the evaluation (at a non-trivial root of -1) of polynomials with small coefficients

**4**

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### “Pseudo-random” subsets of additive bases

**4**

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### Bounds on difference sets of relatively dense A \subseteq {1, …, n}

**4**

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### A question about Erdos thin bases

**3**

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### Inequalities about tripling and doubling sumsets

**3**

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### A new combinatorial problem for finite groups

**3**

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