abstract
##

Can Kirkman's schoolgirls walk abreast by forming arithmetic
progressions ?

Lorenz Halbeisen

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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.