James Propp <propp@math.wisc.edu> writes:

Does the group of order 168 shed any light on the curious fact that the map (x,y) |-> (y,(y+1)/x) (from C(x,y) to itself) is of order 7?

(Another way of stating this fact is that the sequence x,y,(y+1)/x, ((y+1)/x)+1)/y,... satisfying a(n+1) = (a(n)+1)/a(n-1) is periodic with period 7. This sequence is usually attributed to someone named Lyness, but I don't know why Lyness studied it.)

Jim Propp

Are you sure? I get x, y, (y+1)/x, (x+y+1)/(xy), (x+1)/y, x, y, ... with period 5. Cute, the way it follows the same rule forwards as backwards. But of course the rule a(n)+1 = a(n+1)a(n-1) is symmetric. Dan