Intersection Properties of Steiner Systems

Publisher Cayley has established in 1850 that there exist two but no more disjoint Steiner triple systems on a given 7-element set and Kirkman found in the same year that the largest number of disjoint Steiner triple systems of order 9 is seven. But virtually all results of substance in this area that was label “intersection properties of Steiner systems” have been obtained in the last decade. This chapter surveys the present state of affairs in this area. The chapter also discusses some related questions, such as disjoint triple systems with λ > 1, perpendicular Steiner systems and applications to the existence of designs with larger λ.