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Direct Product of Derived Steiner Systems Using Inversive Planes

Published online by Cambridge University Press:  20 November 2018

K. T. Phelps
K. T. Phelps*
Affiliation:
McMaster University, Hamilton, Ontario
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A Steiner system S(t, k, v) is a pair (P, B) where P is a v-set and B is a collection of k-subsets of P (usually called blocks) such that every t-subset of P is contained in exactly one block of B. As is well known, associated with each point x ∈ P is a S(t � 1, k � 1, v � 1) defined on the set Px = P\{x} with blocks

B(x) = {b\{x}|x ∈ b and b ∈ B}.

The Steiner system (Px, B(x)) is said to be derived from (P, B) and is called (obviously) a derived Steiner (t – 1, k – 1)-system. Very little is known about derived Steiner systems despite much effort (cf. [11]). It is not even known whether every Steiner triple system is derived.

Steiner systems are closely connected to equational classes of algebras (see [7]) for certain values of k.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 6 , 01 December 1981 , pp. 1365 - 1369
Copyright
Copyright © Canadian Mathematical Society 1981

References

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