Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-01T01:36:17.554Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)