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On the number of blocks in a perfect covering of υ points

✍ Scribed by Rolf Rees; D.R. Stinson

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
710 KB
Volume
83
Category
Article
ISSN
0012-365X

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✦ Synopsis

In this paper, we study bounds on gck'(v), which denotes the minimum number of blocks to cover every pair of a v-set exactly once, when the largest block has size k.

This bound is exact when v < 2k, but becomes progressively weaker as u increases (for any fixed value of k). A much more powerful bound (in general) was proved by Stanton and Kalbfleisch [lo] (see also [8] and [9]). We refer to this bound as (SK); it states that g'"'(v) z= 1 + k2. (v -k) V-l * * Research supported in part by an NSERC post-doctoral fellowship. ** Research supported in part by NSERC grant A9287.

📜 SIMILAR VOLUMES

On the Number of Blocks in a Generalized
On the Number of Blocks in a Generalized Steiner System
✍ J.H van Lint 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 208 KB

We consider t-designs with \*=1 (generalized Steiner systems) for which the block size is not necessarily constant. An inequality for the number of blocks is derived. For t=2, this inequality is the well known De Bruijn Erdo s inequality. For t>2 it has the same order of magnitude as the Wilson Petr