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arXiv · 1701.08325

A new relationship between block designs

Alexander Shramchenko·Vasilisa Shramchenko
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Abstract

We propose a procedure of constructing new block designs starting from a given one by looking at the intersections of its blocks with various sets and grouping those sets according to the structure of the intersections. We introduce a symmetric relationship of friendship between block designs built on a set $V$ and consider families of block designs where all designs are friends of each other, the so-called friendly families. We show that a friendly family admits a partial ordering. Furthermore, we exhibit a map from the power set of $V$, partially ordered by inclusion, to a friendly family of a particular type which preserves the partial order.

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Alexander Shramchenko, Vasilisa Shramchenko. 2017-01-28. A new relationship between block designs. https://arxiv.org/abs/1701.08325

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