Lattices Associated with a Finite Vector Space

• 作者: Mengtian Yue
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: VECTOR Space GEOMETRIC LATTICE Characteristic POLYNOMIAL
• 年，卷（期）: 2014,（4）
• 页码范围: 672-676
• 页数: 5页
• 分类号: O1

摘要

Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.