Yes that's right. The generalization is in allowing the number of people who meet together at a match to be larger than 2. If you
look here then you will see some schedules for 3 player matches.
If there are
n players, who can be divided exactly into
g groups of
k players for each round, then a necessary condition for a schedule to exist is that (
n-1)/(
k-1) is a whole number. In fact this number gives you the number of rounds in the schedule. So for example the
social square for 16 players in foursomes gives 15/3=5 rounds. Sometimes you will find a pair of numbers
n and
k that pass this test, however the schedule will not exist, for example
n=36,
k=6.
