论文标题
完整拆分图，motzkin单词和分层停车功能上的沙珀模型
The sandpile model on the complete split graph, Motzkin words, and tiered parking functions
论文作者
论文摘要
我们对完整拆分图上的Abelian Sandpile模型（ASM）的复发状态进行了分类。有两种不同的情况要考虑取决于完整拆分图中水槽顶点的位置。降低复发状态的这种表征是用Motzkin单词来表示的，也可以用组合项链来表征。我们还根据称为分层停车功能的新类型的停车功能来对复发状态进行表征。这些停车功能的特征是为每辆汽车分配一层（或颜色），并指定一个希望停放的低层汽车。我们还列举了本文中研究的不同复发配置集，并为此得出了使用BioxtivePrüfer代码参数的完整拆分图的跨越树数的公式。
We classify recurrent states of the Abelian sandpile model (ASM) on the complete split graph. There are two distinct cases to be considered that depend upon the location of the sink vertex in the complete split graph. This characterisation of decreasing recurrent states is in terms of Motzkin words and can also be characterised in terms of combinatorial necklaces. We also give a characterisation of the recurrent states in terms of a new type of parking function that we call a tiered parking function. These parking functions are characterised by assigning a tier (or colour) to each of the cars, and specifying how many cars of a lower-tier one wishes to have parked before them. We also enumerate the different sets of recurrent configurations studied in this paper, and in doing so derive a formula for the number of spanning trees of the complete split graph that uses a bijective Prüfer code argument.
