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Symmetry of iteration graphs

Walter Carlip; Martina Mincheva — 2008

Czechoslovak Mathematical Journal

We examine iteration graphs of the squaring function on the rings $ℤ / n ℤ$ when $n = 2^{k} p$ , for $p$ a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when $k = 3$ and when $k \geq 5$ and are symmetric when $k = 4$ .

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