论文标题
沙珀组和最大稳定配置的兼容复发身份
Compatible Recurrent Identities of the Sandpile Group and Maximal Stable Configurations
论文作者
论文摘要
在Abelian Sandpile模型中，复发性芯片配置引起了人们的关注，因为它们是在减少的Laplacian的商下的自然选择。我们研究了其相对于不同水槽的复发身份相互兼容的图。最大稳定配置是最简单的循环芯片配置，其复发身份等于最大稳定配置的图特别感兴趣，并且据说具有完整的最大身份属性。我们证明，给定任何图形$ g $一个人都可以将树连接到$ g $的顶点，以产生具有完整最大身份属性的图形。我们以几种关于各种图形产品的完整最大身份特性的有趣猜想结束。
In the abelian sandpile model, recurrent chip configurations are of interest as they are a natural choice of coset representatives under the quotient of the reduced Laplacian. We investigate graphs whose recurrent identities with respect to different sinks are compatible with each other. The maximal stable configuration is the simplest recurrent chip configuration, and graphs whose recurrent identities equal the maximal stable configuration are of particular interest, and are said to have the complete maximal identity property. We prove that given any graph $G$ one can attach trees to the vertices of $G$ to yield a graph with the complete maximal identity property. We conclude with several intriguing conjectures about the complete maximal identity property of various graph products.
