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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