A generalized Ramsey number framework is introduced, with polynomial characterizations, and several prime-gap problems are re-expressed as existence of these numbers, largely by construction.
Proceedings of the London Mathematical Soc iety 110(1), 1–18 (2015)
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Ramsey-Theoretic Characterizations of Classically Non-Ramseyian Problems
A generalized Ramsey number framework is introduced, with polynomial characterizations, and several prime-gap problems are re-expressed as existence of these numbers, largely by construction.