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A subset $A$ of a group $G$ is defined to be self-linked if $A\cap gA\ne\emptyset$ for all $g\in G$. This happens if and only if $AA^{-1}=G$. For a finite group $G$ denote by $sl(G)$ the smallest ...

Let $B_n$ be the subset lattice of $\{1,2, \dots , n \}$, also called the boolean lattice of rank $n$. A labeling $f: B_n \to \mathbb{N}_{\ge 1}$ is called acceptable if $\forall a,b \in B_n$: ...