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Results tagged with additive-combinatorics
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user 2083
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.
10
votes
EGZ theorem (Erdős-Ginzburg-Ziv)
Here is what I remember from a proof I came up with long time ago (it appeared in some competitions). I am sure it is known, but since the proof is short, I will put it here:
The statement can be re …
- 30.6k
16
votes
2
answers
2k
views
Sets that are not sum of subsets
Let $\mathcal P$ be the set of finite subsets of $\mathbb Z_{\geq 0}$ , each of them contains $0$. We say that $A \in \mathcal P$ is indecomposable if it is not $B+C$ (the sum set of $B,C$) with $B,C\ …
- 30.6k
10
votes
0
answers
350
views
A formula for Frobenius number of certain numerical semigroups
The old formula for the Frobenius number of a numerical semigroup generated by two elements can be stated as follows: assume $\gcd\{a+1,b+1\}=1$, then the Frobenius number of $S= \left<a+1,b+1\right>$ …
- 30.6k
4
votes
0
answers
155
views
Inequalities about tripling and doubling sumsets
Let $A$ be a set of vectors in $\mathbb Z^d$ who $\mathbb R$-span is the whole $\mathbb R^d$. Let $s_i(A)$ denote the size of $A+A+\dots A$ ($i$ times). I am interested in the following:
Question …
- 30.6k
10
votes
1
answer
286
views
Freiman inequality for projective space?
This question is suggested by some results in a paper I am writing. I would like to write it down there but want to make sure that it is not known or at least MO-hard.
Freiman's inequality states th …
- 30.6k
5
votes
Accepted
Freiman inequality for projective space?
As stated, the answer is no, Freiman's inequality no longer holds. The counter example is $A$ being the vertices of an equilateral triangle on the unit circle. I found this by looking at the proof of …
- 30.6k
19
votes
4
answers
865
views
Size of sets with complete double
Let $[n]$ denote the set $\{0,1,...,n\}$. A subset $S\subseteq [n]$ is said to have complete double if $S+S=[2n]$. Let $m(n)$ be the smallest size of a subset of $[n]$ with complete double. My questio …
- 30.6k