Combinatorial designs with applications. Notes (Q2810315)

This short monograph provides a gentle and very readable introduction to combinatorial designs. Chapter 1 provides a basic foundation for understanding combinatorial designs. It introduces balanced incomplete block designs, Latin squares, orthogonal arrays, projective and affine planes, symmetric designs, difference sets, group-divisible designs, and pairwise designs. Chapter 2 then examines Steiner triple systems in somewhat more detail, introducing a few of the main threads of investigation (automorphisms, resolvability, colourings, subsystems, to name a few). Chapter 3 then considers a next natural case, the Steiner systems with block size four and strength 2, in order to illustrate the extension of some results from Steiner triple systems. Chapter 4 considers a related but different extension, to the Steiner systems with block size four and strength 3, or Steiner quadruple systems. Finally, Chapter 5 introduces further variations, including cycle systems, graph decompositions, Room squares, and Howell designs.NEWLINENEWLINEThe presentation is well thought out, and well presented. Any reader who is new to the area will find a good introduction to pursue further study, and readers with some knowledge in the area will find useful connections made among the many topics discussed.