Vector spaces as unions of proper subspaces
Commutative Algebra
2015-02-02 v4 Combinatorics
Abstract
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.
Cite
@article{arxiv.0803.2746,
title = {Vector spaces as unions of proper subspaces},
author = {Apoorva Khare},
journal= {arXiv preprint arXiv:0803.2746},
year = {2015}
}
Comments
8 pages, LaTex; to appear in "Linear Algebra and its Applications"