On the structure of the $h$ -fold sumsets

Let~$A$ be a set of nonnegative integers. Let~$(h A)^{(t)}$ be the set of all integers in the sumset~$hA$ that have at least~$t$ representations as a sum of~$h$ elements of~$A$. In this paper, we prove that, if~$k \geq 2$, and~$A=\left\{a_{0}, a_{1}, \ldots, a_{k}\right\}$ is a finite set of integers such that~$0=a_{0}

Keywords:

• Structure (category theory)
• Finite set
• Combinatorics
• Mathematics

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