# Questions tagged [sidon-sets]

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10 questions
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### Optimize / simple Set Covering Problem

Let $k,m\in\mathbb{N}$ be given. Let $M:=\{0,... , m-1\}$. How to find a subset $T\subset M$, $|T|=k$ such that $|T+T|$ is maximal, where $T+T=\{ (a+b)\mathbin\%m \mid a\in T,b\in T \}$ (“%” means ...
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### Lower bound for k-fold Sidon Sets

k-fold Sidon set is defined in http://www.combinatorics.org/ojs/index.php/eljc/article/view/v10i1r25/pdf (page #4, paragraph 4) Does anyone know what the best known lower bound construction is for the ...
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### Recovering Sidon sets from difference sets

How can I recover a Sidon set $A\subseteq \mathbb{Z}/n\mathbb{Z}$ from the set $A-A\subseteq \mathbb{Z}/n\mathbb{Z}$? Is it even unique? (up to translation and reflection) ($A-A$ stands for the set ...
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### Has anyone studied Golomb rulers having a spectrum with a minimal $L^2$ norm?

A Golomb ruler can be described as a set of marks on a line having integer positions, such that no two pairs of marks are separated by the same distance. Call the spectrum of a ruler the (multi-)set ...
### $B_k[1]$ sets with smallest possible $m = max B_k[1]$ for given $k$ and $n = |B_k[1]|$ elements
Sidon sets are sets $A \subset \mathbb{N}$ such that for all $a_j,b_j \in A$ holds $$a_1+a_2=b_1+b_2 \iff \{a_1,a_2\}=\{b_1,b_2\}$$ Thus if you know the sum of two elements, you know which elements ...
### Number of $b$-separated Sidon sets with pairwise difference set intersection bounds
Given two integers integers $0<b<p$ and a real $\alpha\in(0,1)$ call a set of $m$ integers $a_1<\dots<a_m$ in the interval $(p^\alpha,p-p^\alpha)$ to be $b$-separated Sidon if: \$a_i-a_j\...