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A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups

✍ 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.


πŸ“œ SIMILAR VOLUMES


A quintessential proof of van der Waerde
✍ George Mills πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 362 KB

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.

Proof of a Conjecture of BollobΓ‘s and Ko
✍ Yoshiyasu Ishigami πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 242 KB

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) .