MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Olof Heden, in his work "A survey of the different types of vector space partitions", discusses various results regarding the following qustion - given a vector space $V$ over a finite field, how can we partition it into a set $\mathcal P$ of vector spaces, such that every $v\in V,v\ne 0$ belongs to exactly one member of $\mathcal P$? I'm interseted in a generalization of this work to covering any general subset of a vector space over a finite field by not only vector spaces, but also affine spaces. Is anyone familiar with a work done on this subject?

share|cite|improve this question
    
Do you have any restrictions on the kind of covering you want (minimum number of spaces, say?) After all, every single point of $F_q^n$ is an affine subspace. – Klaus Draeger Feb 27 '12 at 13:52
    
Ofcourse. I'm looking for the minimum cover. Although any other result could be useful as well. – Netanel Feb 28 '12 at 9:28

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.