Some remarks on sumsets and restricted sumsets

摘要

Let A be a ?nite set of integers. For any integer h ≥ 1, let h-fold sumset hA be the set of all sums of h elements of A and let h-fold restricted sumset h∧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 ?nite integer set. In details, we give the best lower bound for the cardinality of restricted sumsets 2∧A and 3∧A and also discuss the cardinality of restricted sumset h∧A.