In this paper we continue the study of right-angled Artin groups up to commensurability initiated in [CKZ]. We show that RAAGs defined by different paths of length greater than 3 are not commensurable. We also characterise which RAAGs defined by paths are commensurable to RAAGs defined by trees of diameter 4. More precisely, we show that a RAAG defined by a path of length n > 4 is commensurable to a RAAG defined by a tree of diameter 4 if and only if n ≡ 2 (mod 4). These results follow from the connection that we establish between the classification of RAAGs up to commensurability and linear integer-programming.

中文翻译：

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关于直角 Artin 组 II 的可公度性：由路径定义的 RAAG

在本文中，我们继续研究直角 Artin 群，直至在 [CKZ]。我们表明，由长度大于 3 的不同路径定义的 RAAG 是不可比较的。我们还描述了哪些由路径定义的 RAAG 与由直径为 4 的树定义的 RAAG 相当。更准确地说，我们表明由长度为的路径定义的 RAAGn> 4 与由直径为 4 的树定义的 RAAG 可公度当且仅当n≡ 2（模 4）。这些结果源于我们在 RAAG 分类到可公度性和线性整数规划之间建立的联系。