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キーワード:
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要旨:
We reveal a connection between the incompressibility method and the Lov\'{a}sz
local lemma in the context of Ramsey theory.
We obtain bounds by repeatedly encoding objects of interest and thereby
compressing strings. The method is demonstrated on the example of van der
Waerden numbers.
In particular we reprove that $w(k;c) \geq \frac{c^{k-3}}{k} \cdot
\frac{k-1}{k}$.
The method is applicable to obtain lower bounds of Ramsey numbers, large
transitive subtournaments and other Ramsey
phenomena as well.
