A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups
β Scribed by Shtern, A I
- Book ID
- 115512066
- Publisher
- Turpion Limited
- Year
- 2008
- Tongue
- English
- Weight
- 470 KB
- Volume
- 72
- Category
- Article
- ISSN
- 1064-5632
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A particularly well suited induction hypothesis is employed to give a short and relatively direct formulation of van der Waerden's argument which establishes that for any partition of the natural numbers into two classes, one of the classes contains arbitrarily long arithmetic progressions.
For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .