Special sum set
= Special sum set
A finite <set> $A$ of <positive integers> such that nonempty <disjoint sets> contained in $A$ have different <sums>, and the larger subset has the larger <sum> when their sizes differ. For $a_1<\cdots<a_n$, the size condition is equivalent to $a_1+\cdots+a_{k+1}>a_{n-k+1}+\cdots+a_n$ for $1\le k\le\lfloor(n-1)/2\rfloor$: the left side is the smallest possible sum of $k+1$ elements and the right side the largest sum of $k$ elements.