Monochromatic Progressions in Random Colorings

Details Monochromatic Progressions in Random Colorings Monochromatic Progressions in Random Colorings

2011-06-04

arxiv.org/abs/1106.0793v1

Mathematics

Combinatorics

5 pages

Scientific paper

Let N^{+}(k)= 2^{k/2} k^{3/2} f(k) and N^{-}(k)= 2^{k/2} k^{1/2} g(k) where 1=o(f(k)) and g(k)=o(1). We show that the probability of a random 2-coloring of {1,2,...,N^{+}(k)} containing a monochromatic k-term arithmetic progression approaches 1, and the probability of a random 2-coloring of {1,2,...,N^{-}(k)} containing a monochromatic k-term arithmetic progression approaches 0, for large k. This improves an upper bound due to Brown, who had established an analogous result for N^{+}(k)= 2^k log k f(k).

Affiliated with

Also associated with

No associations

Rating

Monochromatic Progressions in Random Colorings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Monochromatic Progressions in Random Colorings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monochromatic Progressions in Random Colorings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-7099