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Identifying Half-Twists Using Randomized Algorithm Methods

机译:使用随机算法方法识别半扭曲

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Since the braid group was discovered by Artin (1947), the question of its conjugacy problem has been solved by Garside (1969) and Birman et al. (1998). However, the solutions given thus far are difficult to compute with a computer, since the number of operations needed is extremely large. Meanwhile, random algorithms used to solve difficult problems such as the primality of a number were developed, and the random practical methods have become an important tool. We give a random algorithm, along with a conjecture of how to improve its convergence speed, in order to identify elements in the braid group, which are conjugated to its generators (say σ_1~κ) for a given power k. These elements of the braid group, the half-twists, are important in themselves, as they are the key players in some geometrical and algebraical methods, the building blocks of quasipositive braids and they construct endless sets of generators for the group.
机译:自从Artin(1947)发现辫子群以来,其共轭性问题已由Garside(1969)和Birman等人解决。 (1998)。但是,由于所需的操作数量非常大,因此迄今为止给出的解决方案很难用计算机来计算。同时,开发了用于解决诸如数字素数之类的难题的随机算法,并且随机实用方法已经成为重要的工具。我们给出了一个随机算法,以及一个如何提高其收敛速度的猜想,以便识别出编织组中的元素,这些元素在给定的功率k下与生成器共轭(例如σ_1〜κ)。辫子组的这些元素(半绕线)本身很重要,因为它们是某些几何和代数方法的关键参与者,是准正辫子的基本组成部分,它们为该组构造了无穷的生成器集。

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