On Optimal M-Sets Related to Motzkin’s Problem

الملخص EN

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.