# 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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### Inequality in the proof of Roth's theorem on progressions

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### Bounding the size of certain sumsets in the plane

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### Lemma towards Roth's theorem

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### Separating points of shifts of a finite set in the plane

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### Density of intersection with shifted sets

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### Smallest $k$ such that every vector is a linear combination of at most $k$ generators

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### Partition set into equal-sum subsets

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### Properties of Zero Line-Sum Matrices

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### large arithmetic progression modulo p (II)

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

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### Large arithmetic progression modulo $p$

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### Near-linear mappings from $\mathbb F_p$ to $\mathbb R$

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### Disjoint union of affine subspaces contains a larger affine subspace

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### Increasing sequences in polynomial progressions modulo p

**10**

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### Which of these sums appear most often?

**4**

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### Smallest size of integral vector with certain inner product

**6**

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### Binary weight of shifted integers

**3**

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### Questions on “The condition number of a randomly perturbed matrix”

**2**

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### A question about finite free convolution

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### Large submatrices of circulant matrices

**5**

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### A question about the paper “The Condition Number of a Randomly Perturbed Matrix”

**1**

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### Generating larger atoms from smaller ones in a simple $\text{C}_0$-monoid

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### On finite subsets of set of integers, which lies in its sum-set , whose sum of elements equals $0$ [duplicate]

**11**

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### Optimality of the Plünnecke-Ruzsa Inequality

**5**

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### Maximum-sized product sets in infinite groups

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### Are there unique additive decompositions of the reals?

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### The product of the clique and independence numbers in the Cayley sum graph

**10**

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### Positive integer combination of non-negative integer vectors

**2**

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### Large additive energy, and numbers having many representations as differences

**39**

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### Sets of unit fractions with sum $\leq 1$

**4**

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### Upper Bound on minimum number of lattice points

**12**

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### Partition of [3n] into summoids

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### Growth in a vector space

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### Complete residue system modulo n (permutation of numbers 0 to n-1) such that

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### sum over partitions

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### Linear combination of characters

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### Divisibility labeling on a boolean lattice and nonzero Euler totient

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### Request for reference for some proofs about Gowers' norm

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### Decomposing a finite group as a product of subsets

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### On point sets with many distinct distances

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### The set of lengths of $nX$ gets larger and larger for every non-zero, non-empty, finite $X \subseteq \mathbf N$ with $0 \in X$

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### Large cubes in sum/difference sets

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### Additive basis of subexponential growth

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### Large gaps in Singer's difference sets

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### What's known about $X$ when $|X(n) + X(n)| < kn$, $n \in \mathbb{N}$, absolute constant $k$?

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### Limit measuring failure of sum-set cancellability

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### In how many different ways can the sumset of a Sidon set be ordered?

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### Difference bases in simple cyclic groups

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### Lower bound for sumset in discrete cube

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