401 and Beyond: Improved Bounds and Algorithms for the Ramsey Algebra Search
Jeremy F. Alm
Department of Mathematics
Illinois College
Jacksonville, IL 62650
USA
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 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
