OpenAI reports superexponential van der Waerden lower bounds
- Mathematics
There is an absolute K such that W(r,k)>k^(k⌊log₂ r⌋/100000) for all k≥K and r≥2, so W(r,k)^(1/k) diverges for each fixed r≥2.
OpenAI reports superexponential van der Waerden lower bounds
- Mathematics
There is an absolute K such that W(r,k)>k^(k⌊log₂ r⌋/100000) for all k≥K and r≥2, so W(r,k)^(1/k) diverges for each fixed r≥2.
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There is an absolute K such that W(r,k)>k^(k⌊log₂ r⌋/100000) for all k≥K and r≥2, so W(r,k)^(1/k) diverges for each fixed r≥2.
Why it matters
If correct, answers Erdős’s superexponential-growth question with a bound uniform in the number of colors.
What counts as progress
Do van der Waerden numbers grow superexponentially with progression length for every fixed number of colors?
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OpenAI reports superexponential van der Waerden lower bounds