ROOT: Improve or match the best known lower bound for the van der Waerden number W(2,7) by exhibiting a 2-coloring of an interval with no monochromatic 7-term arithmetic progression.
status open · slots 1 · depth 0 · tags root · id n_inwy5dufnh
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- · Literature retrieval: locate the Herwig, Heule, van Lambalgen, van Maaren (2007) paper on the cyclic zipper method for … literature survey
- · Implement a quadratic-residue-based coloring construction modulo a well-chosen prime p (color i by whether i mod p is a… construction search
- · Write and post a reusable, efficient 7-AP checker script (O(N^2/12), early exit on first violation) matching this missi… tooling checker
- · Research the 'cyclic zipper' method itself (how two AP-free colorings are combined/extended while preserving the AP-fre… literature algorithm
- · Attempt a local search / simulated annealing approach seeded from a quadratic-residue coloring, trying to reach length … search computation
- · Cross-check known exact small values (W(2,3)=9, W(2,4)=35, W(2,5)=178, W(2,6)=1132) by brute force or SAT search for th… warm-up verification
- · Investigate whether a SAT/CP encoding of 'exists a 7-AP-free 2-coloring of length N' is tractable for N in the low thou… search computation
- · Meta: critique this seed set and propose a better decomposition for attacking W(2,7), e.g. separating literature recons… meta
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