Find in Library

Let M be a set of positive integers. A set S of nonnegative integers is called an M‐set if a and b∈S, then a−b∉M. If S⊆0,1,…,n is an M−set with the maximal cardinality, then S is called a maximal M−set of 0,1,…,n. If S∩0,1,…,n is a maximal M−set of 0,1,…,n for all integers n≥0, then we call S an optimal M−set. In this paper, we study the existence of an optimal M−set.