A note on Fibonacci-type polynomials
Tewodros Amdeberhan
本文研究了由递推关系 $G_n=x^kG_{n-1}+G_{n-2}$ 定义的一类斐波那契型多项式的最大实根的收敛性。
我们选择研究由 $G_n=x^kG_{n-1}+G_{n-2}$ 给出的某些斐波那契型多项式的最大实根的收敛性。特殊情况 $k=1$ 和 $k=2$ 分别见于文献[4]和[7]。
We opt to study the convergence of maximal real roots of certain Fibonacci-type polynomials given by $G_n=x^kG_{n-1}+G_{n-2}$. The special cases $k=1$ and $k=2$ are found in [4] and [7], respectively.
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In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k sequences of the generalized order-k Fibonacci and Pell numbers.
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A common generalization of Dickson polynomials, Fibonacci polynomials, and Lucas polynomials and applications
本文定义了满足线性递推关系的更一般的多变量多项式族，给出了显式公式和行列式表达式，并将其应用于2阶递推多项式，揭示了Fibonacci、Lucas和Dickson多项式等的关系与恒等式，是对多项研究的统一推广。
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Powerful Fibonacci polynomials over finite fields
本文研究了有限域上斐波那契多项式及广义卢卡斯多项式成为完全幂或强大多项式的特征。
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本研究聚焦形式幂级数领域，探讨可作为偶/奇下标斐波那契、卢卡斯多项式插值的形式幂级数，拓展了相关多项式的幂级数研究方向。
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本文定义了广义Fibonacci多项式上的单纯形$d$-多胞形数，建立了基本恒等式与$q$-恒等式，求出了生成函数及倒数之和，并引入了相应的Zeta函数。
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研究Fibonacci多项式F_n(x)和Lucas多项式L_n(x)的不可约因子的单生成性，证明对所有奇数n，F_n(x)的不可约因子是单生成的；对所有偶数n，L_n(x)的不可约因子是单生成的。
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本研究推广了一道面向高中生的拉马努金习题，得到的结果可作为$x^n-1$因式分解公式的变体，丰富了相关数论习题的结论。
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Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials
本文利用 Dickson 多项式与分圆域的联系，证明了广义 $(k,t)$-Fibonacci 和 $(k,t)$-Lucas 多项式不可约因子生成数域的单项性，并推广至经典 Fibonacci、Lucas 及 Chebyshev 多项式。
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Fibonacci sums and divisibility properties
本文利用 Sury 多项式恒等式的变体推导有限斐波那契与卢卡斯和的新表达式，并将其推广到相关多项式及 Horadam 序列，进而用于发现和证明整除性质。
Polynomial values with integer coefficients of the generating functions for Fibonacci polynomials
本文将Fibonacci序列生成函数取整数值的判别结果推广到满足带系数递推关系的Fibonacci多项式，并在$\sqrt d$代入时给出同形式结论。
Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs
本文利用斐波那契数列和切比雪夫多项式，计算轮图图表（即辫子闭包）的约化Fox着色群及Alexander-Burau-Fox模，推广了相关结果。
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We study a family of finite--dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type $\tt A_2^{(2)}$. We prove that these modules admit a decreasing filtration whose sections are isomorphic to stable Demazure modules in an integrable highest weight module of sufficiently large level. In particular, we show that any stable level $m'$ Demazure module admits a filtration by level $m$ Demazure modules for all $m\ge m'$. We define the graded and weighted generating functions which encode the multiplicity of a given Demazure module and establish…
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On certain Fibonacci representations
本文探讨如何利用 Fibonacci 数生成其他递归序列，将某些整数递归序列族表示为 Fibonacci 数的有理多项式线性组合。
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