“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 12156 |
|
||||
| Abstract: | |||||
|
Let X be a v-set, \B a set of 3-subsets (triples) of X, and \B+∪\B− a partition of \B with |\B−|=s.
The pair (X,\B) is called a simple signed Steiner triple system, denoted by ST(v,s), if the number of occurrences of every 2-subset of X in triples B ∈ \B+ is one more than the number of occurrences in triples B ∈ \B−.
In this paper we prove that \st(v,s) exists if and only if v ≡ 1,3 mod 6, v ≠ 7, and s ∈ {0,1,…,sv−6,sv−4,sv}, where sv=v(v−1)(v−3)/12 and for v=7, s ∈ {0,2,3,5,6,8,14}.
Download TeX format |
|||||
| back to top | |||||
