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CONSTRUCTION TECHNIQUES FOR ANTI-PASCH STEINER TRIPLE SYSTEMS

Published online by Cambridge University Press:  01 June 2000

A. C. H. LING ,
C. J. COLBOURN ,
M. J. GRANNELL  and
T. S. GRIGGS
A. C. H. LING
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
C. J. COLBOURN
Affiliation:
Department of Computer Science, Votey Building, University of Vermont, Burlington, VT 05405, USA
M. J. GRANNELL
Affiliation:
Department of Pure Mathematics, Open University, Walton Hall, Milton Keynes MK7 6AA
T. S. GRIGGS
Affiliation:
Department of Pure Mathematics, Open University, Walton Hall, Milton Keynes MK7 6AA
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Abstract

Four methods for constructing anti-Pasch Steiner triple systems are developed. The first generalises a construction of Stinson and Wei to obtain a general singular direct product construction. The second generalises the Bose construction. The third employs a construction due to Lu. The fourth employs Wilson-type inflation techniques using Latin squares having no subsquares of order 2. As a consequence of these constructions we are able to produce anti-Pasch systems of order v for v 31 or 7 (mod 18), for v ≡ 49 (mod 72), and for many other values of v.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 641 - 657
Copyright
The London Mathematical Society 2000

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