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Quadratic cyclic sequences
Monatshefte für Mathematik ( IF 0.9 ) Pub Date : 2020-08-06 , DOI: 10.1007/s00605-020-01454-z
Paul Baird , Ali Fardoun , Zeina Ghazo Hanna

We explore relations between cyclic sequences determined by a quadratic difference relation, cyclotomic polynomials, Eulerian digraphs and walks in the plane. These walks correspond to closed paths for which at each step one must turn either left or right through a fixed angle. In the case when this angle is $2 \pi /n$, then non-symmetric phenomena occurs for $n\geq 12$. Examples arise from algebraic numbers of modulus one which are not $n$'th roots of unity.

中文翻译:

二次循环序列

我们探索由二次差分关系、分圆多项式、欧拉有向图和平面中的游走确定的循环序列之间的关系。这些步行对应于封闭的路径,在每个步骤中,人们必须向左或向右转一个固定的角​​度。在这个角度为 $2 \pi /n$ 的情况下,则 $n\geq 12$ 会出现非对称现象。例子来自模一的代数数,它们不是单位的第 n 个根。
更新日期:2020-08-06
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