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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Let $p$ be prime and $\mathbb{F}_p$ the finite field with $p$ elements. Suppose we have a set $B\subseteq \mathbb{F}_p$ satisfying $|B|<p^{\alpha}$ for some $0<\alpha<1$ and there exists $A\... 0answers 91 views ### Bell polynomial with variables 1 and 0 Let$B_{n,k}(x_1,\cdots,x_{n-k+1})$be the Bell polynomial. If$x_1=\cdots=x_{n-k+1}=1$, we know that$B_{n,k}(x_1,\cdots,x_{n-k+1})=S(n,k)$, where$S(n,k)$is the Stirling number of second kind. ... 1answer 159 views ### Unique representation and sumsets Let$A$be a finite, nonempty subset of an abelian group, and let$2A:=\{a+b\colon a,b\in A\}$and$A-A:=\{a-b\colon a,b\in A\}$denote the sumset and the difference set of$A$, respectively. If ... 1answer 143 views ### What are the consequence of Snevily's conjecture to analytic number theory if really there is a connection between them? [closed] Snevily's conjecture it is an open conjecture in Group theory for non cyclic Group and it were proved for abelian groups of prime order using a fairly standard application of the Alon-Tarsi ... 1answer 158 views ### Average size of iterated sumset modulo$p-1$, Given a prime$p$, what is the average size of the iterated sumset,$|kA|$, modulo$p-1$, with$p$a prime, and$k$given, with$A$chosen at random? You can pick any type of prime you like for$p$, ... 1answer 245 views ### Does$g+A\subseteq A+A$imply$g\in A$? Suppose that$A$is a subset of a (large) finite cyclic group such that$|A|=5$and$|A+A|=12$. Given that$g$is a group element with$g+A\subseteq A+A$, can one conclude that$g\in A$? 3answers 509 views ### Does the expression$x^4 +y^4$take on all values in$\mathbb{Z}/p\mathbb{Z}$? As the title asks: does there exist$N$such that, for any prime$p$larger than$N$, the expression$x^4 +y^4$takes on all values in$\mathbb{Z}/p\mathbb{Z}$? I have been thinking about this ... 1answer 173 views ### Finite concatenation-free languages Suppose,$A$is a finite alphabet.$L \subset A^*$is a language. Let's call$L$concatenation-free iff$\forall u, v \in L$we have$uv \notin L$. Does there exist some function$c: \mathbb{N} \...
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Does anybody have access to the paper A. Kotzig: On well spread sets of integers, 1972, or does anybody know the proof of $\sigma^*(n)\geq 4+\binom{n-1}2$ for $n\geq7$ (as cited in Marr,Wallis: Magic ...
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### What is the “right” notion of exponentiation in $\beta \mathbb N$?
The Stone–Čech compactification $\beta \mathbb N$ of the positive integers has extensive applications in combinatorial number theory. A feature of $\beta \mathbb N$ that makes these applications ...