abstract
Can Kirkman's schoolgirls walk abreast by forming arithmetic
progressions ?
Lorenz Halbeisen
A Kirkman triple system of order v, whose point set is
consecutively numbered, is called smooth, if for each parallel
class there is a number d, such that each triple of the parallel
class forms an arithmetic progression modulo v with common
difference d. It will be shown that smooth Kirkman triple systems
of order v exist, if and only if v is a power of 3.