论文标题
有限的平面，曲折序列，斐波那契数，Artin的猜想和三项式
Finite Planes, Zigzag Sequences, Fibonacci Numbers, Artin's Conjecture and Trinomials
论文作者
论文摘要
我们首先考虑了主要特征的基本阿贝尔群体的忠实矩阵表示。认为所考虑的表示形式被确定为单个数字的基础更改。研究这个数字会导致一个新的多项式家族，这些家族具有许多特殊的特性。这些多项式满足三个任期递归，并且与曲折零序列密切相关。解释“ Prime” 1的多项式产生了经典的Morgan-Voyce多项式，该多项式形成了多项式的双交家族，并且在电阻研究中具有应用。对多项式多项式的研究揭示了与斐波那契序列的深入联系，斐波那契序列中质数的出现顺序，环状基团的元素，元素的元素，Artin对原始根部的猜想以及在有限领域的三通基因分解。
We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The representations considered are seen to be determined up to change of bases by a single number. Studying this number leads to a new family of polynomials which exhibit a number of special properties. These polynomials satisfy a three term recursion and are closely related to zigzag zero-one sequences. Interpreting the polynomials for the "prime" 1 yields the classical Morgan-Voyce polynomials, which form twoorthogonal families of polynomials and which have applications in the study of electrical resistance. Study of the general polynomials reveals deep connections with the Fibonacci series, the order of appearance of prime numbers in the Fibonacci sequence, the order of elements in cyclic groups, Artin's conjecture on primitive roots and the factorization of trinomials over finite fields.
