论文标题
沿斐波那契甚至是（几乎）可实现的
Fibonacci along even powers is (almost) realizable
论文作者
论文摘要
如果整数序列是某些地图的周期点计数，则称为可实现。 fibonacci序列$（f_n）$没有此属性，沿正方形$（f_ {n^2}）$采样的斐波那契序列也没有此属性。我们证明，这是与斐波那契序列的判别性相关的算术现象，它通过证明序列$（5f_ {n^2}）$是可实现的。更普遍地，我们表明$（f_ {n^{2k-1}}）$在特别强的意义上是无法实现的，而$（5f_ {n^{2k}}）$对于任何$ k \ ge1 $都是可实现的。
An integer sequence is called realizable if it is the count of periodic points of some map. The Fibonacci sequence $(F_n)$ does not have this property, and the Fibonacci sequence sampled along the squares $(F_{n^2})$ also does not have this property. We prove that this is an arithmetic phenomenon related to the discriminant of the Fibonacci sequence, by showing that the sequence $(5F_{n^2})$ is realizable. More generally, we show that $(F_{n^{2k-1}})$ is not realizable in a particularly strong sense while $(5F_{n^{2k}})$ is realizable, for any $k\ge1$.
