论文标题
斐波那契多项式
Fibonacci polynomials
论文作者
论文摘要
fibonacci多项式$ \ big \ {f_n（x）\ big \} _ {n \ ge 0} $已通过多种方式进行了研究。在本文中，我们通过Viennot堆的理论来研究它们。在此设置中，我们的多项式构成基础$ \ big \ {p_n（x）\ big \} _ {n \ ge 0} $，$ p_n（x）$ n $ $ n $。给出了这一点，我们被迫设置$ p_n（x）= f_ {n+1}（x）$。堆设置扩展了三个项递归给出的正交多项式的经典理论的flajolet视图。因此，对于我们的$ p_n（x）$的大部分身份，可以通过组合参数得出。使用当前的设置，我们得出了各种新身份。我们必须提到，这里提出了堆的理论。这是处理斐波那契多项式所需的要多得多。我们这样做是为了传达堆的力量。在讲义中，有一章致力于堆，其中大多数内容都致力于该理论的应用。
The Fibonacci polynomials $\big\{F_n(x)\big\}_{n\ge 0}$ have been studied in multiple ways. In this paper we study them by means of the theory of Heaps of Viennot. In this setting our polynomials form a basis $\big\{P_n(x)\big\}_{n\ge 0}$ with $P_n(x)$ monic of degree $n$. This given, we are forced to set $P_n(x)=F_{n+1}(x)$. The Heaps setting extends the Flajolet view of the classical theory of orthogonal polynomials given by a three term recursion. Thus with Heaps most of the identities for our $P_n(x)'s$ can be derived by combinatorial arguments. Using the present setting we derive a variety of new identities. We must mention that the theory of Heaps is presented here without restrictions. This is much more than needed to deal with the Fibonacci polynomials. We do this to convey a flavor of the power of Heaps. In the lecture notes there is a chapter dedicated to Heaps where most of its contents are dedicated to applications of the theory.
