Correction to ‘d-partition geometries’

✍ Scribed by Lynn Margaret Batten

• Publisher: Springer
• Year: 1981
• Tongue: English
• Weight: 72 KB
• Volume: 11
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00149362

✦ Synopsis

In this note, we correct a result given in [1]. There we claim-PP8-that if 33 is a d-partition geometry then any pair of (d + 1)-related flats with nonempty intersection actually have intersection a d-flat. This is easily seen to be incorrect by considering the following example: 33 is a 3-flat with precisely five points. The lines are all two-point sets, and the planes all three-point sets. Since any two coplanar lines are, in fact, incident, it is easy to see that 33 is a 1-partition geometry. However, it is also easy to find two planes intersecting in precisely one point. My thanks to W. M. Kantor for pointing this out.

By adding an extra condition, we arrive at PP8' : If33 is a d-partition geome-