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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Pasch Trades on the Projective Triple System of Order 31

M. J. Grannell1, M. Knor2
1Department of Mathematics The Open University, Walton Hall Milton Keynes MK7 6AA UNITED KINGDOM
2Department of Mathematics Faculty of Civil Engineering Slovak University of Technology Radlinského 11 813 68 Bratislava SLOVAKIA
  • Published: 29/02/2016

Abstract

We determine all 120 nonisomorphic systems obtainable from the projective Steiner triple system of order 31 by at most three Pasch trades. Exactly three of these, each corresponding to three Pasch trades, are rigid. Thus three Pasch trades suffice, and are required, in
order to convert the projective system of order 31 to a rigid system. This contrasts with the projective system of order 15 where four Pasch trades are required. We also show that four Pasch trades are required in order to convert the projective system of order 63 to a
rigid system.

Keywords: Pasch configuration; Projective triple system; Steiner triple sys- tem; Trade.
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Citation
M. J. Grannell, M. Knor. Pasch Trades on the Projective Triple System of Order 31[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 096. 23-31. DOI: .