Simple Signed Steiner Triple Systems |
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| Authors: | E Ghorbani G B Khosrovshahi |
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| Institution: | 1. Department of Mathematics, K. N. Toosi University of Technology, , Tehran, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), , Tehran, Iran;3. Department of Mathematics, Statistics and Computer Science, University of Tehran, , Iran |
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| Abstract: | Let X be a v‐set,  be a set of 3‐subsets (triples) of X, and  be a partition of  with  . The pair  is called a simple signed Steiner triple system, denoted by ST , if the number of occurrences of every 2‐subset of X in triples  is one more than the number of occurrences in triples  . In this paper, we prove that  exists if and only if  ,  , and  , where  and for  ,  . © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 332–343, 2012 |
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| Keywords: | simple signed Steiner triple system trade |
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