NDLI: A census of highly symmetric combinatorial designs

Content Provider	Springer Nature Link
Author	Huber, Michael
Copyright Year	2007
Abstract	As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t=2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t>2 most of these characterizations have remained long-standing challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 3≤t≤6 is of particular interest and has been open for about 40 years (cf. Delandtsheer (Geom. Dedicata 41, p. 147, 1992 and Handbook of Incidence Geometry, Elsevier Science, Amsterdam, 1995, p. 273), but presumably dating back to 1965). The present paper continues the author’s work (see Huber (J. Comb. Theory Ser. A 94, 180–190, 2001; Adv. Geom. 5, 195–221, 2005; J. Algebr. Comb., 2007, to appear)) of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.
Ending Page	476
Page Count	24
Starting Page	453
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	4
Volume Number	26
Language	English
Publisher	Springer US
Publisher Date	2007-04-17
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Finite automorphism groups of algebraic, geometric, or combinatorial structures Steiner designs Convex and Discrete Geometry 3-homogeneous permutation groups Computer Science Steiner systems Block designs Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Flag-transitive group of automorphisms Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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