The Lyness is R.C. Lyness, HM Inspector of Schools in Britain for many years. The original reference is no doubt somewhere in the Math Gaz, to which he contributed extensively. His son, James Lyness, was a Singapore colleague, who arrived on this continent soon after I did. R. On Wed, 13 Nov 2002, James Propp wrote:

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

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