Cycles and divergent trajectories for a class of permutation sequences

John L Simons

Let $f$ be a permutation from ${\mathbb{N}}_0$ onto ${\mathbb{N}}_0$. Let $x\in {\mathbb{N}}_0$ and consider a (finite or infinite) sequence $s=(x,f(x),f^2(x),\cdots )$. We call $s$ a per…