Table of Contents
International Journal of Combinatorics
Volume 2016 (2016), Article ID 7092474, 6 pages
http://dx.doi.org/10.1155/2016/7092474
Research Article

A New Relationship between Block Designs

179-337 Moskovsky pr., Saint Petersburg 196084, Russia
2Department of Mathematics, University of Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1

Received 15 April 2016; Accepted 29 June 2016

Academic Editor: Jean-Yves Thibon

Copyright © 2016 Alexander Shramchenko and Vasilisa Shramchenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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 , partially ordered by inclusion, to a friendly family of a particular type which preserves the partial order.