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.