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Paper   IPM / M / 12156
School of Mathematics
  Title:   Simple signed Steiner triple systems
1.  E. Ghorbani
2.  G. B. Khosrovshahi
  Status:   Published
  Journal: J. Combin. Des.
  Year:  2012
  Pages:   DOI: 10.1002/jcd.21297
  Supported by:  IPM
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}.

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