AI 中文总结
本文研究球形型阿廷群的德霍诺伊结构相关条件，证明其A条件几乎总是成立但B条件很少满足，明确了这类群具备德霍诺伊结构的条件情况。
AI 中文摘要
德霍诺伊结构是用于在加尔斯德群G中得到左序的工具，Arcis与Paris引入了A条件和B条件，两者均满足时可确保G具有德霍诺伊结构，这两个条件描述了对应幺半群中的乘积如何与交替分解相关。本文研究球形型阿廷群G的情况，证明A条件几乎总是成立，但B条件很少满足。
英文摘要
A Dehornoy structure is a tool used to obtain a left order in the Garside group~$G$. Arcis and Paris introduced two conditions, known as Condition~$A$ and Condition~$B$. When they are both satisfied, they ensure that~$G$ possesses a Dehornoy structure. These two conditions describes how the product in the corresponding monoid behaves with an alternating decomposition. Here, we consider the case of a spherical type Artin group~$G$. We prove that Condition A almost always holds, but Condition~$B$ is rarely satisfied.
