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Pasch trades on the projective triple system of order 31

Grannell, Mike and Knor, Martin (2016). Pasch trades on the projective triple system of order 31. Journal of Combinatorial Mathematics and Combinatorial Computing, 96 pp. 23–32.

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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.

Item Type: Journal Item
ISSN: 0835-3026
Keywords: Pasch configuration; Projective triple system; Steiner triple system; Trade
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 46817
Depositing User: Mike Grannell
Date Deposited: 18 Jul 2016 14:11
Last Modified: 01 May 2019 18:42
URI: http://oro.open.ac.uk/id/eprint/46817
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