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On Optimal M-Sets Related to Motzkin’s Problem

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Listed:
  • Quan-Hui Yang
  • Ting Pan
  • Jian-Dong Wu
  • Li Guo

Abstract

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.

Suggested Citation

  • Quan-Hui Yang & Ting Pan & Jian-Dong Wu & Li Guo, 2020. "On Optimal M-Sets Related to Motzkin’s Problem," Journal of Mathematics, Hindawi, vol. 2020, pages 1-5, December.
    • Handle: RePEc:hin:jjmath:7457625
    DOI: 10.1155/2020/7457625
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