Lattices Associated with a Finite Vector SpaceReport as inadecuate




Lattices Associated with a Finite Vector Space - Download this document for free, or read online. Document in PDF available to download.

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.

KEYWORDS

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

Source: http://www.scirp.org/



DOWNLOAD PDF




Related documents