A variant of the Hales-Jewett theorem
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Date: 10-09-2007
Start Time:
4:00pm
End Time: 5:00pm
Speaker: Jozsef Solymosi , University of British Columbia
Location: 725 CEPSR
ABSTRACT
The Hales-Jewett theorem is a central result in Ramsey Theory. It states that for every m and n natural numbers ther is a threshold, N = N (m, n), such that for any partition of [0, 1, ..., n − 1] N into m classes there is a class containing a combinatorial line.
We present a variant of the Hales-Jewett theorem for n = 3. This variant gives a much better bound on N than the best known bound for Hales-Jewettand it is still strong enough for many applications. For example we show that for any coloring of the first L natural numbers using not more than log log L colors, there is always a monochromatic geometric progression of length three.
Joint work with Ron Graham.
BIO
For more information on Dr. Solymosi, please visit this site.