Men's-Room Permutations

[Neil Fernandez]

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.

LOL! :-)

>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).

<snip>

>I get, by hand (so I may have erred), the number of such permutations
>(using rule 2), for m =1,2,3,...:
>1, 2, 4, 8, 24, 36,...

 From this I assume that the line is straight :-)

For an arrangement in a circle, I get:

1,2,6,8,60,72,...

Not sure what happens on an Archimedean spiral with equation r = theta,
with urinals spaced at multiples of constant angle phi.

Neil

-- 
Neil Fernandez