Characterizing Geometric Designs
- We conjecture that the classical geometric 2-designs formed by the points and d-dimensional subspaces of the projective space of dimension n over the field with q elements, where 2 <= d <= n-1, are characterized among all designs with the same parameters as those having line size q+1. The conjecture is known to hold for the case d=n-1 (the Dembowski-Wagner theorem) and also for d=2 (a recent result established by Tonchev and the present author). Here we extend this result to the cases d=3 and d=4. The general case remains open and appears to be difficult.
| Author: | Dieter JungnickelORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-11243 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1341 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2009-35) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2009/12/23 |
| Tag: | block design; finite projective space |
| GND-Keyword: | Geometrische Figur; Blockplan; Endlicher projektiver Raum |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
