Men's-Room Permutations and other interpretations

[Olivier Gerard]

I think there are many potential interpretations of this 
sequence and similar ones.  For example, the way people
sit in a train: they tend to sit the further apart possible,
on separate banks, most of them oriented toward the destination
of the train, etc.  overcoming progressively these tendencies
as the car gets more and more crowded.  There is something
like phase transitions at certain density levels.

Versions with various kinds of multisets
and plane partitions instead of permutations
would be relevant or more precise in certain cases.

I have often wondered at the fact that the rules seems
inverse for people waiting for the train on a booth:

They tend to aggregate themselves to whatever little groups
already exist, and there are few isolates for a long time.
Most of them look in the direction opposite to their
destination, trying to see the train coming in advance.

Any idea on how to design other sequences about this ?

Olivier


In message <E1BeHKQ-0003Gv-00 at blount.mail.mindspring.net>, Leroy Quet
<qq-quet at mindspring.com> writes
> 
> >I was, seriously, inspired by a line of urinals in a men's-room
> >to come up with this sequence.
> 
> >Assume that the men in a men's-room wanting to relieve
> >themselves are all rather modest about using the urinals.
> >
> >They will, when other men are already using some of the urinals,
> >each tend to use the urinal farthest from any other occupied urinal
> >(or use one of these most-lonely urinals if there is a tie for
> >loneliest urinal).
>