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Wang, K.S. and Li, Z.T. (2008) Lattices Associated with Vector Spaces Over a Finite Field. Linear Algebra and Its Applications, 429, 439-446. http://dx.doi.org/10.1016/j.laa.2008.02.035

has been cited by the following article:

• TITLE: Lattices Associated with a Finite Vector Space

  AUTHORS: Mengtian Yue

  KEYWORDS: Vector Space; Geometric Lattice; Characteristic Polynomial

  JOURNAL NAME: Applied Mathematics, Vol.5 No.4, March 10, 2014

  ABSTRACT: 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.