Results 1 to 4 of 4

Math Help - finite field version of the Bollobás theorem

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    8

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by kp3004 View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    8
    Quote Originally Posted by tonio View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by kp3004 View Post
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Splitting Field of a Polynomial over a Finite Field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 1st 2011, 03:45 PM
  2. Finite Field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 23rd 2010, 02:19 AM
  3. Finite Field
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 15th 2010, 02:25 AM
  4. Finite field
    Posted in the Advanced Algebra Forum
    Replies: 18
    Last Post: August 28th 2009, 07:26 PM
  5. Finite Field
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 9th 2009, 09:08 PM

Search Tags


/mathhelpforum @mathhelpforum