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Decompositions of Difference Sets

โœ Scribed by Dieter Jungnickel; Vladimir D Tonchev

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
122 KB
Volume
217
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We characterize those symmetric designs with a Singer group G which admit a quasi-regular G-invariant partition into strongly induced symmetric subdesigns. In terms of the corresponding difference sets, the set associated with the larger design can be decomposed into a difference set describing the small designs and a suitable relative difference set. This generalizes the decomposition of the classical design ลฝ . with the complements of hyperplanes in PG m y 1, q as blocks into sub-designs ลฝ . arising from PG d y 1, q whenever d divides m. Parametrically, these geometrical examples provide the only known examples of the situation we are studying. But there are many nonisomorphic examples with the same parameters, namely the complements of the classical GMW designs and some generalizations. We also discuss the possibilities for obtaining new difference sets in this way and point out a connection to the recent constructions of Ionin for symmetric designs. แฎŠ 1999 Academic Press * Research partially supported by a research grant of the Alexander von Humboldt Foundation.

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