Author Topic: Project DONE  (Read 227 times)

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Offline StyM

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Project DONE
« on: 29 October, 2016, 10:55:49 PM »

 

Offline stoneageman

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Re: Project DONE
« Reply #1 on: 30 October, 2016, 08:42:30 PM »
 <::>
Oh well, easy come, easy go  )&^
 

Offline stoneageman

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Re: Project DONE
« Reply #2 on: 16 December, 2016, 10:08:02 PM »
For posterity  /<^

"Sorry for my recent inactivity. A paper has been posted on arxiv for this project at https://arxiv.org/abs/1603.03301  and has been submitted for publication. I would like to thank all the volunteers who contributed their resources to this project. The project will no longer generate new work, but will incorporate any results received"

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This project found improved lower bounds for van der Waerden numbers. The number W(k,r) is the length of the shortest sequence of colors with r different colors that guarantees an evenly-spaced subsequence (or arithmetic progression) of the same color of length k. We applied existing techniques: Rabung's using primitive roots of prime numbers and Herwig et al's Cyclic Zipper Method as improved by Rabung and Lotts. We used much more computing power, 2 teraflops, using distributed computing and larger prime numbers, through over 500 million, compared to 10 million by Rabung and Lotts. We used r up to 10 colors and k up to length 25, compared to 6 colors and length 12 in previous work. Our lower bounds on W(k,r) grow roughly geometrically with a ratio converging down towards r for r equals 2, 3, and 4. We conjecture that the exact numbers W(k,r) grow at the rate r for large k.
« Last Edit: 16 December, 2016, 10:11:08 PM by stoneageman »