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Simple Signed Steiner Triple Systems
Author(s) -
Ghorbani E.,
Khosrovshahi G. B.
Publication year - 2012
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21297
Subject(s) - mathematics , combinatorics , steiner system , simple (philosophy) , partition (number theory) , set (abstract data type) , discrete mathematics , computer science , philosophy , epistemology , programming language
Let X be a v ‐set, B be a set of 3‐subsets (triples) of X , andB + ∪ B −be 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 , . . . , s v − 6 , s v − 4 , s v } , wheres v = v ( v − 1 ) ( v − 3 ) / 12 and for v = 7 , s ∈ { 0 , 2 , 3 , 5 , 6 , 8 , 14 } . © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 332–343, 2012