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On the optimal structure of recovering set pairs in lattices: the sandglass conjecture

✍ Scribed by Rudolf Ahlswede; Gábor Simonyi

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
312 KB
Volume
128
Category
Article
ISSN
0012-365X

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✦ Synopsis

We present a conjecture concerning the optimal structure of a subset pair satisfying two dual requirements in a lattice that can be derived as the product of k finite length chains. The conjecture is proved for k = 2.

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## Abstract In this paper, we study the problem of constructing sets of __s__ latin squares of order __m__ such that the average number of different ordered pairs obtained by superimposing two of the __s__ squares in the set is as large as possible. We solve this problem (for all __s__) when __m__