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An -(sub)set is a (sub)set with elements. For integers , a Steiner system is an -set and a set of -subsets having the property that any -subset of is contained in exactly one -set in . For example, if , a Steiner system is a set of -sets, called hexads, with the property that any set of elements of is contained in (can be completed to'') exactly one hexad. This note focuses on . If is a Steiner system of type in a -set then the symmetric group of sends to another Steiner system of . It is known that if and are any two Steiner systems of type in then there is a such that . In other words, a Steiner system of this type is unique up to relabelings. (This also implies that if one defines to be the stabilizer of a fixed Steiner system of type in then any two such groups, for different Steiner systems in , must be conjugate in . In particular, such a definition is well-defined up to isomorphism.)
Next: Curtis' kitten Up: MINIMOGs and Mathematical blackjack Previous: MINIMOGs and Mathematical blackjack
David Joyner
2000-05-29