• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.667-673
• /
• 2019

Let A be a finite set of integers. For any integer $h{\geq}1$, let h-fold sumset hA be the set of all sums of h elements of A and let h-fold restricted sumset $h^{\wedge}A$ be the set of all sums of h distinct elements of A. In this paper, we give a survey of problems and results on sumsets and restricted sumsets of a finite integer set. In details, we give the best lower bound for the cardinality of restricted sumsets $2^{\wedge}A$ and $3^{\wedge}A$ and also discuss the cardinality of restricted sumset $h^{\wedge}A$.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.305-313
• /
• 2021

Let h ≥ 2 and A = {a0, a1, …, ak-1} be a finite set of integers. It is well-known that |hA| = hk - h + 1 if and only if A is a k-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets A with some extremal the cardinalities of hA.