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Wan, Z. and Huo, Y. (2004) Lattices Generated by Transitive Sets of Subspaces Under Finite Classical Groups. 2nd Edition, Science Press, Beijing.

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.