"unknown" and "not_applicable"

[Peter Cameron]

The permutation rank *is* defined for an intransitive group - it is just
the number of orbits on ordered pairs.

Actually it is a bit difficult to think of an example where not_applicable
would be required. THe options, it seems to me, are to delete it altogether,
or to use it as a complicated way of signalling something (which would have
to be specified carefully in each case) - e.g. a convention that
resolvable is not_applicable if k doesn't divide v but must be boolean or
unknown if k divides v.

The problem with the latter approach is where to stop. A rather contrived
example of this would be that a 2-design cannot be resolvable unless it
satisfies Bose's inequality b \ge v+r-1. ("Contrived" because I can't think
of a parameter set with k dividing v satisfying Fisher's inequality but not
Bose's.)

Peter.