Thread: finite field version of the Bollobás theorem

The proof of Bollobas's theorem on subspaces uses the fact that we can factor out by a subspace in general position. This requires that the Field is infinite. How can I prove the finite field version of the theorem?

Originally Posted by kp3004

The proof of Bollobas's theorem on subspaces uses the fact that we can factor out by a subspace in general position. This requires that the Field is infinite. How can I prove the finite field version of the theorem?

Several things are called Bollobas's theorem. Try the following: http://iti.mff.cuni.cz/series/files/iti305.pdf

Tonio

Originally Posted by tonio

Several things are called Bollobas's theorem. Try the following: http://iti.mff.cuni.cz/series/files/iti305.pdf

Tonio

I'm referring to theorem 1.1 in your document.
How do I prove the finite field version of it?

Originally Posted by kp3004

I'm referring to theorem 1.1 in your document.
How do I prove the finite field version of it?

Hmmm...theorem 1.1 is a purely combinatoric one , no fields or vector spaces whatsoever mentioned. perhaps you mean theorem 1.3, or maybe 1.4? If 1.3 then, as it's written there, Lovasz proved it and a reference to one of his papers is at the end of the file (and pay attention that this theorem is for "arbitrary fields"), and if you meant 1.4 then it is proved in that paper and it's for FINITE fields....I think this all pretty much covers what you wanted, doesn't it?!

tonio