论文标题
关于标尺序列的普遍性
On the ubiquity of the ruler sequence
论文作者
论文摘要
尺子函数或GROS序列是一个经典的无限整数序列，它正在引起一些有趣的数学问题。在本文中，我们提供了包含这种类型序列的四个新问题：（i）人口统计学的动力学自动机，（ii）中间间隔Cantor集合，（iii）通过重复多边形和（iv）Feigenbaum Cascade累积点的水平可见性序列的构造。在所有这些中，Infinte序列是通过复制的递归程序获得的。统治者序列的特性，尤其是与递归性和自我含义有关的特性，用于更深入地了解这四个问题。统治者序列的这些新表示可以激发离散数学领域的新研究。
The ruler function or the Gros sequence is a classical infinite integer sequence that is underlying some interesting mathematical problems. In this paper, we provide four new problems containing this type of sequence: (i) a demographic discrete dynamical automata, (ii) the middle interval Cantor set, (iii) the construction by duplication of polygons and (iv) the horizontal visibility sequence at the accumulation point of the Feigenbaum cascade. In all of them, the infinte sequence is obtained by a recursive procedure of duplication. The properties of the ruler sequence, in particular, those relating to recursiveness and self-containing, are used to get a deeper understanding of these four problems. These new representations of the ruler sequence could inspire new studies in the field of discrete mathematics.
