论文标题
关于有限连接的架子的猜想
On a conjecture about profiles of finite connected racks
论文作者
论文摘要
机架是具有二进制操作的集合，使得左乘法是该集合的自动形态，而一个问题是满足特定条件的机架。对于有限连接的机架，由元素左乘法定义的置换的循环类型独立于所选元素。此周期类型称为机架的轮廓。 Hayashi猜想，在有限连接的问题的轮廓中，一个循环的长度必须划分最大循环的长度。在本文中，我们在某些特定情况下证明了Hayashi的猜想。
A rack is a set with a binary operation such that left multiplications are automorphisms of the set and a quandle is a rack satisfying a certain condition. For a finite connected rack the cycle type of the permutation defined by left multiplication by an element is independent from the chosen element. This cycle type is called the profile of the rack. Hayashi conjectured, in the profile of a finite connected quandle, the length of a cycle must divide the length of the largest cycle. In this paper, we prove Hayashi's Conjecture in some particular cases.
