2017/07/23 by Keranen, Melissa S., Kreher, Donald L.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.07282
A partial Steiner triple system whose triples can be partitioned into s partial parallel classes, each of size m, is a signal set, denoted SS(v,s,m). A Kirkman signal set KSS(v,m) is an SS(v,s,m) with s=\lfloorμ(v)/m\rfloor. When v ≡ 1 or 3 \pmod6, then μ(v)=b, so the decomposition of an STS(v) into partial parallel classes of size m is equivalent to a KSS(v,m). Table of known existence results is given.