Most of these problems were presented at the problem session of the 19th British Combinatorial Conference at the University College of North Wales, Bangor, 29 June–4 July 2001. I have added some problems given to me after the session. As previously, the problems are circularly ordered; you may start at any point. Problem 1 (BCC19.1) Tight single-change covering designs. Proposed by D. A. Preece...

We study a design and optimization problem that occurs, for example, when single nucleotide polymorphisms (SNPs) are to be genotyped using a universal DNA tag array. The problem of optimizing the universal array to avoid disruptive cross-hybridization between universal components of the system was addressed in previous work. Cross-hybridization can, however, also occur assay specifically, due t...

Abstract Methods for improving upper and lower bounds various coverings of planar sets are proposed. New numbers partition constituents presented, suggestions the generalization presented methods offered.