Open Mathematics (Dec 2020)

A study on strongly convex hyper S-subposets in hyper S-posets

  • Tang Jian,
  • Xie Xiang-Yun,
  • Davvaz Bijan

DOI
https://doi.org/10.1515/math-2020-0127
Journal volume & issue
Vol. 18, no. 1
pp. 1935 – 1951

Abstract

Read online

In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.

Keywords