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A computational exploration of Polynomial van der Waerden numbers

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polyvdw

A computational exploration of Polynomial van der Waerden numbers

Methods and results can be found in TeX or PDF format.

Results

  • Proved there exists an elementary configuration bounding PW(4, {x^2}) < 1+290085289^2
  • Proved there exists an elementary configuration bounding PW(4, {x^2+x}) < 1+113261*113262
  • Proved there exist elementary configurations bounding PW(4, {ax^2+bx}) for all a=1, b <= 2000, and some with a > 1 see here
  • Proved that there exist elementary configurations bounding PW(3, {ax^2+bx})
  • Found a "Pythagorean K4" for {x^2+x}

Instructions

First, adjust output path OUT_PATH in PolyRunner and ThreeColorRunner. To run, compile from the src/java directory with javac polyvdw/*.java. Then run the 4-color version with java polyvdw/PolyRunner or the 3-color version with java polyvdw/ThreeColorRunner.

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A computational exploration of Polynomial van der Waerden numbers

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