Flag-transitive Steiner Designs (Frontiers in Mathematics) by Michael Huber

By Michael Huber

The characterization of combinatorial or geometric constructions when it comes to their teams of automorphisms has attracted massive curiosity within the final a long time and is now usually considered as a normal generalization of Felix Klein’s Erlangen program(1872).Inaddition,especiallyfor?nitestructures,importantapplications to sensible subject matters reminiscent of layout thought, coding conception and cryptography have made the ?eld much more appealing. the subject material of this examine monograph is the learn and sophistication- cation of ?ag-transitive Steiner designs, that's, combinatorial t-(v,k,1) designs which admit a bunch of automorphisms appearing transitively on incident point-block pairs. because of the classi?cation of the ?nite uncomplicated teams, it's been attainable in recent times to represent Steiner t-designs, often for t=2,adm- ting teams of automorphisms with su?ciently robust symmetry houses. For Steiner 2-designs, arguably the main basic effects were the classi?cation of all aspect 2-transitive Steiner 2-designs in 1985 through W. M. Kantor, and the just about whole decision of all ?ag-transitive Steiner 2-designs introduced in 1990 byF.Buekenhout,A.Delandtsheer,J.Doyen,P.B.Kleidman,M.W.Liebeck, and J. Saxl. although, regardless of the classi?cation of the ?nite basic teams, for Steiner t-designs witht> 2 many of the characterizations of those forms have remained long-standing difficult difficulties. Speci?cally, the decision of all ?- transitive Steiner t-designs with three? t? 6 has been of specific curiosity and item of study for greater than forty years.

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Flag-transitive Steiner Designs (Frontiers in Mathematics)

The characterization of combinatorial or geometric constructions by way of their teams of automorphisms has attracted significant curiosity within the final a long time and is now as a rule considered as a traditional generalization of Felix Klein’s Erlangen program(1872). Inaddition,especiallyfor? nitestructures,importantapplications to useful subject matters corresponding to layout conception, coding thought and cryptography have made the ?

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