论文标题
非古典线性倾斜度序列和循环多项式
Non-classical linear divisibility sequences and cyclotomic polynomials
论文作者
论文摘要
分序序列由其元素在索引时相互划分的属性定义。也满足线性复发的序列序列，例如斐波那契数，是由多项式产生的，这些序列将其组成与每个正整数幂分开。我们使用标记的Hasse图将这些多项式分解为循环多项式，并根据它们构建新的整数划分序列。我们还表明，与斐波那契数不同，这些非经典序列没有强大的分裂性。
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials that divide their compositions with every positive integer power. We completely characterize such polynomials in terms of their factorizations into cyclotomic polynomials using labeled Hasse diagrams, and construct new integer divisibility sequences based on them. We also show that, unlike the Fibonacci numbers, these non-classical sequences do not have the property of strong divisibility.
