# 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 $?

**46**

**5**answers

### Jean Bourgain's Relatively Lesser Known Significant Contributions

**45**

**3**answers

### Number of elements in the set $\{1,\cdots,n\}\cdot\{1,\cdots,n\}$

**39**

**4**answers

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

**34**

**3**answers

### Lagrange four squares theorem

**33**

**4**answers

### Cliques, Paley graphs and quadratic residues

**26**

**2**answers

### The Erdős-Turán conjecture or the Erdős' conjecture?

**26**

**3**answers

### long enough interval of integers to solve a simultaneous congruence

**25**

**3**answers

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

**24**

**2**answers

### Partitions to different parts not exceeding $n$

**23**

**3**answers

### How many different numbers can be obtained as product of first $n$ natural numbers?

**23**

**3**answers

### Are sets with similar asymptotic behavior as the primes necessarily finite additive bases?

**23**

**1**answer

### Arithmetic Progressions of Squares

**23**

**1**answer

### Two conjectures about zero inner products and dissociated sets

**23**

**1**answer

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

**23**

**0**answers

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

**23**

**0**answers

### probability of zero subset sum

**22**

**1**answer

### Monochromatic triangles in every two-coloring of the plane?

**21**

**1**answer

### Avoiding multiples of $p$

**20**

**3**answers

### A sumset inequality

**20**

**2**answers

### EGZ theorem (Erdős-Ginzburg-Ziv)

**20**

**4**answers

### Arithmetic progressions inside polynomial sets

**19**

**4**answers

### Number of vectors so that no two subset sums are equal

**19**

**3**answers

### Can nonabelian groups be detected “locally”?

**18**

**3**answers

### The sum of integers being a bijection

**18**

**3**answers

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

**18**

**3**answers

### An “Average” Erdős–Turán conjecture

**16**

**2**answers

### Roth's theorem and Behrend's lower bound

**16**

**3**answers

### What is the shortest route to Roth's theorem?

**15**

**3**answers

### Is there an “analytical” version of Tao's uncertainty principle?

**15**

**1**answer

### Goldbach-type theorems from dense models?

**15**

**4**answers

### Are all partial consecutive harmonic subsums distinct?

**15**

**1**answer

### Combinatorics problem about sum of natural numbers

**15**

**1**answer

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

**15**

**1**answer

### The hypercube: $|A {\stackrel2+} E| \ge |A|$?

**14**

**3**answers

### When does $P(a−b)=0$ for $a≠b$ ensure $P(0)=0$? (Continued.)

**14**

**3**answers

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

**14**

**1**answer

### What is the smallest cardinality of a self-linked set in a finite cyclic group?

**14**

**1**answer

### On the $L^1$-norm of certain exponential sums.

**14**

**1**answer

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

**14**

**1**answer

### Erdös-Turán via Hardy-Littlewood circle method?

**13**

**3**answers

### Density of all n such that 2^n-1 is square free

**13**

**3**answers

### Zero-sum partition of an abelian group

**13**

**1**answer

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

**13**

**1**answer

### Coin problem with permutations

**13**

**0**answers

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

**13**

**0**answers

### Correlation of Fourier transforms of characteristic functions

**12**

**2**answers

### Did Erdős publish his proof of the multiplicative version of the Erdős-Turán conjecture?

**12**

**1**answer

### Where did the term “additive energy” originate?

**12**

**1**answer