论文标题
Farey单词及其痕迹的组合
The combinatorics of Farey words and their traces
论文作者
论文摘要
我们介绍了一个3个可赚的“多项式”一家，这些家族与$ 3 $ manifolds和orbifolds的几何形状和拓扑密切相关，因为它们可用于生成边界和本地坐标的具体实现，以实现kleinian组的一级差异空间。因此，这个多项式家族具有许多相当出色的特性。我们从抽象的组合观点研究了这些多项式，包括递归定义扩展了文献中为歧管特殊情况所知的递归定义，甚至超出了几何形状的预测。我们还提出了一些有趣的例子和猜想，我们希望引起对代数组合和超几何功能感兴趣的研究人员的注意。 本文的结果还为对PSL（2，C）等级两个亚组的各种分类问题提供了一种实用的方法，因为它们与作者最近的其他作品一起，使某些团体是离散且免费的，有效的方法来识别Relators的证书。
We introduce a family of 3-variable "Farey polynomials" that are closely connected with the geometry and topology of $3$-manifolds and orbifolds as they can be used to produce concrete realisations of the boundaries and local coordinates for one-complex-dimensional deformation spaces of Kleinian groups. As such, this family of polynomials has a number of quite remarkable properties. We study these polynomials from an abstract combinatorial viewpoint, including a recursive definition extending that which is known in the literature for the special case of manifolds, even beyond what the geometry predicts. We also present some intriguing examples and conjectures which we would like to bring to the attention of researchers interested in algebraic combinatorics and hypergeometric functions. The results in this paper additionally provide a practical approach to various classification problems for rank-two subgroups of PSL(2,C) since they, together with other recent work of the authors, make it possible to provide certificates that certain groups are discrete and free, and effective ways to identify relators.
