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How to find a set $A \subset \mathbb{N}$ such that any sum of at most three Elements $a_i \in A$ is different if at least one element in the sum is different. Example with $|A|=3$: Out of the set $A :... 0answers 52 views ###$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 ... 3answers 694 views ### Selecting$k$integers from an interval$[0, N]$to maximize the minimum difference between pairwise sums I have an optimization problem where I need to select$k$integers over the interval$[0, N]$s.t. I maximize the minimum difference between any pairwise sum of the$k$integers (where we also include ... 1answer 264 views ### Recovering Sidon sets from difference sets, part 2. This is inspired by a recent question. A set$A \subset \mathbb{Z}/n\mathbb{Z}$with$|A|=m$is a Sidon set if all the pairwise sums of distinct elements are unequal:$A+A=\{a+a' \mid a,a' \in A, a \...
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 ...
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 ...