Characterizing Geometric Designs II
- We provide a characterization of the classical geometric designs formed by the points and lines of the projective space PG(n,q) of dimension n over the field with q elements, where n >= 3, among all non-symmetric (v,k,1)-designs as those with the maximal number of hyperplanes. As an application of this result, we also characterize the classical quasi-symmetric designs formed by the points and (n-2)-dimensional subspaces of PG(n,q), where n >= 4, among all (not necessarily quasi-symmetric) designs with the same parameters as those having line size q+1 and sufficiently large intersection numbers. Finally, we also give an explicit lower bound for the number of non-isomorphic designs having the same parameters as the classical point-line designs; in particular, we obtain a new proof for the known fact that this number grows exponentially for any fixed value of q.
| Author: | Dieter JungnickelORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-11257 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1342 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2009-36) |
| 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 |
