Forbes, Anthony; Grannell, Mike and Griggs, Terry
(2007).
*Rendiconti del Circolo Matematico di Palermo Serie II*, 56, pp. 17–32.

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## Abstract

Quattrochi and Rinaldi introduced the idea of - isomorphism between Steiner systems. In this paper we study this concept in the context of Steiner triple systems. The main result is that for any positive integer , there exists such that for all admissible and for each STS (say ), there exists an STS (say ) such that for some , is strictly -isomorphic to . We also prove that for all admissible , there exist two STSs which are strictly -isomorphic. Define the distance between two Steiner triple systems and of the same order to be the minimum volume of a trade which transforms into a system isomorphic to . We determine the distance between any two Steiner triple systems of order 15 and, further, give a complete classification of strictly -isomorphic and -isomorphic pairs of STSs.

Item Type: | Article |
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ISSN: | 0009-725X |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 22759 |

Depositing User: | Mike Grannell |

Date Deposited: | 18 Aug 2010 12:38 |

Last Modified: | 04 Oct 2016 10:42 |

URI: | http://oro.open.ac.uk/id/eprint/22759 |

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