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Rigid Steiner Triple Systems Obtained from Projective Triple Systems
Author(s) -
Grannell M. J.,
Knor M.
Publication year - 2014
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.21357
Subject(s) - steiner system , mathematics , projective test , combinatorics , permutation (music) , identity (music) , automorphism , triple system , automorphism group , triple play (telecommunications) , discrete mathematics , pure mathematics , computer science , telecommunications , art , aesthetics
It was shown by Babai in 1980 that almost all Steiner triple systems are rigid; that is, their only automorphism is the identity permutation. Those Steiner triple systems with the largest automorphism groups are the projective systems of orders2 n − 1 . In this paper, we show that each such projective system may be transformed to a rigid Steiner triple system by at most n Pasch trades whenever n ≥ 4 .