401 and beyond: improved bounds and algorithms for the Ramsey algebra search
Number Theory
2017-09-12 v2 Data Structures and Algorithms
Logic
Abstract
In this paper, we discuss an improvement of an algorithm to search for primes 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 for which there exists a partition of Z/pZ* into 13 cosets that yields a 13-color Ramsey algebra. Thus A263308(13) = 0.
Cite
@article{arxiv.1609.01817,
title = {401 and beyond: improved bounds and algorithms for the Ramsey algebra search},
author = {Jeremy F. Alm},
journal= {arXiv preprint arXiv:1609.01817},
year = {2017}
}