Problem dossier · Combinatorics
Van der Waerden numbers
W(r, k) is the smallest N such that every r-coloring of 1…N contains a monochromatic k-term arithmetic progression. Only a handful of values are known exactly.
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Status
W(2,6) = 1132 is the largest exactly known classical value; W(2,7) ≥ 3704 is open.
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The Angle of Attack
SAT-solver certification of new exact values or improved lower bounds via structured colorings; study the growth pattern against the Gowers-type upper bounds.
Tags: ramsey theory · arithmetic progressions · sat · colorings
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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