Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.4

401 and Beyond: Improved Bounds and Algorithms for the Ramsey Algebra Search

Jeremy F. Alm
Department of Mathematics
Illinois College
Jacksonville, IL 62650


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 obtain, 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.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A263308.)

Received September 11 2016; revised version received August 29 2017. Published in Journal of Integer Sequences, August 31 2017.

Return to Journal of Integer Sequences home page