On the Number of Blocks in a Generalized Steiner System
On the Number of Blocks in a Generalized Steiner System
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关于广义 Steiner 系统中的块数
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. H. Lint
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文献类型：
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作者：
J. H. Lint
我们的设计与？= 1（广义Steiner系统），其中块大小不一定是常数。一个不等式的块的数量推导出来。Fort=2，这个不等式就是著名的De Bruijn？埃尔多？s不等式。福特>2它有相同的数量级的威尔逊？常块大小Steiner系统的Petrenjuk不等式。这篇文章的要点是，这个不等式很容易推导出来，而且似乎并不为人所知。1969年，伍德尔（J.伦敦数学学会）推导出了一个更强的不等式。(2)1，509？519），但它需要拉格朗日乘数的证明。
We considert-designs with?=1 (generalized Steiner systems) for which the block size is not necessarily constant. An inequality for the number of blocks is derived. Fort=2, this inequality is the well known De Bruijn?Erdo?s inequality. Fort>2 it has the same order of magnitude as the Wilson?Petrenjuk inequality for Steiner systems with constant block size. The point of this note is that the inequality is very easy to derive and does not seem to be known. A stronger inequality was derived in 1969 by Woodall (J. London Math. Soc.(2)1, 509?519), but it requires Lagrange multipliers in the proof.