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arXiv · 1609.01817

401 and beyond: improved bounds and algorithms for the Ramsey algebra search

Jeremy F. Alm
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Abstract

In this paper, we discuss an improvement of an algorithm to search for primes $p$ and coset-partitions of Z/pZ* that yield Ramsey algebras over Z/pZ. We also prove an upper bound on the modulus p in terms of the number of cosets. We have, as a corollary, that there is no prime $p$ for which there exists a partition of Z/pZ* into 13 cosets that yields a 13-color Ramsey algebra. Thus A263308(13) = 0.

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Jeremy F. Alm. 2016-09-07. 401 and beyond: improved bounds and algorithms for the Ramsey algebra search. https://arxiv.org/abs/1609.01817

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