论文标题
Q构造的整数衍生自副整数及其应用
q-deformed integers derived from pairs of coprime integers and its applications
论文作者
论文摘要
与群集代数，蛇形图和Q-Integers有关，Kyungyong Lee和Ralf Schiffler最近发现了一个用于计算（归一化的）Jones Jones多项式链接的公式，以持续的分数扩展有理数。 Sophie Morier-Genoud和Valentin Ovsienko引入了Q呈现的持续分数，并表明，通过使用它们，A_N类型A_N的归一化琼斯多项式计数的每个系数。在本文中，我们介绍了由成对的副整体定义的Q构造的整数，这些整数是由分母和其Q呈现的Q构造的分子持续的持续分数所激发的，并给出了计算（归一化的）琼斯多项式链接的有效算法。研究了由成对的副整数定义的Q-智能者的各种特性，并显示了其应用。
In connection with cluster algebras, snake graphs and q-integers, Kyungyong Lee and Ralf Schiffler recently found a formula for computing the (normalized) Jones polynomials of rational links in terms of continued fraction expansion of rational numbers. Sophie Morier-Genoud and Valentin Ovsienko introduced q-deformed continued fractions, and showed that by using them each coefficient of the normalized Jones polynomial counted quiver representations of type A_n. In this paper we introduce q-deformed integers defined by pairs of coprime integers, which are motivated by the denominators and the numerators of their q-deformed continued fractions, and give an efficient algorithm for computing the (normalized) Jones polynomials of rational links. Various properties of q-integers defined by pairs of coprime integers are investigated and shown its applications.
