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


Vector Space; Geometric Lattice; Characteristic Polynomial

Cite this paper

Yue, M. 2014 Lattices Associated with a Finite Vector Space. Applied Mathematics, 5, 672-676. doi: 10.4236-am.2014.54064.

Author: Mengtian Yue



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