A General Recursive Construction for Quadruple Systems
A General Recursive Construction for Quadruple Systems
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DOI：
10.1016/0097-3165(82)90001-2
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发表时间：
1982-09
期刊：
影响因子：
--
通讯作者：
Alan Hartman
中科院分区：
文献类型：
--
作者：
Alan Hartman
A Steiner-quadruple system of order υ is an ordered pair (X,Q), whereXis a set of cardinality υ, andQis a set of 4-subsets ofX, called blocks, with the property that every 3-subset ofXis contained in a unique block. In this paper we show that if there exists a quadruple system of orderVwith a subsystem of order υ, then there exists a quadruple system of order 3V− 2υwith subsystems of ordersVand υ. Hanani has given a proof of this result forυ= 1, and in a previous paper, the author has proved the case whenV≡ 2υ(mod 6). The construction given here proves all remaining cases, and has many applications to other existence problems for 3-designs.
