𝔖 Bobbio Scriptorium
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Orbits of infinite block designs

✍ Scribed by Bridget S. Webb

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
332 KB
Volume
169
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let ~ be a 2- (v,k,2) design with k finite. When v is finite it is well known that blocktransitivity implies point-transitivity, whereas for infinite designs the relationship between the numbers of point and block orbits is unknown. We find bounds for the number of block and point orbits and provide a combinatorial proof generalising the result of Cameron that a Steiner triple system has at least as many block orbits as point orbits. We generalise some results of Camina on block-transitive designs and find an upper bound for the point rank.

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