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Paper IPM / M / 12156  


Abstract:  
Let X be a vset, \B a set of 3subsets (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 2subset 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,…,s_{v}−6,s_{v}−4,s_{v}}, where s_{v}=v(v−1)(v−3)/12 and for v=7, s ∈ {0,2,3,5,6,8,14}.
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