On Partitions of Finite vector Spaces
Combinatorics
2009-02-19 v1 Group Theory
Abstract
In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that, if V is a finite vector space over a field of order q, then the number of the subspaces of minimum dimension t of a non-trivial partition of V is greater than or equal to q+t. Moreover, we give some extensions of a well known Beutelspacher-Heden's result on existence of T-partitions.
Cite
@article{arxiv.0902.3075,
title = {On Partitions of Finite vector Spaces},
author = {Antonino Giorgio Spera},
journal= {arXiv preprint arXiv:0902.3075},
year = {2009}
}
Comments
14 pages