The Abelian sandpile model on Ferrers graphs - A classification of recurrent configurations
The Abelian sandpile model on Ferrers graphs - A classification of recurrent configurations
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DOI：
10.1016/j.ejc.2019.05.008
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
M. Dukes;T. Selig;Jason P. Smith;E. Steingrímsson
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文献类型：
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作者：
M. Dukes;T. Selig;Jason P. Smith;E. Steingrímsson
我们对阿贝尔沙堆模型(ASM)在Ferrers图上的所有循环构型进行了分类。分类依据的是EW-Tableaux的装饰，未装饰的是具有最小循环构型的双射。我们引入了装饰排列，推广到装饰EW-Tableaux，给出了装饰排列和排列之间的双射，给出了装饰排列和ASM的所有循环构型之间的直接双射。我们还描述了Postnikov的装饰排列和不传递树之间的双射，它的广度优先搜索对应于相应构型的正则倾倒。
We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are in bijection with the minimal recurrent configurations. We introduce decorated permutations, extending to decorated EW-tableaux a bijection between such tableaux and permutations, giving a direct bijection between the decorated permutations and all recurrent configurations of the ASM. We also describe a bijection between the decorated permutations and the intransitive trees of Postnikov, the breadth-first search of which corresponds to a canonical toppling of the corresponding configurations.