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.

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Author:Dieter JungnickelORCiDGND
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-35)
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