单圈图上Abelian沙堆模型的雪崩大小(英文)  

Avalanche Sizes of the Abelian Sandpile Model on Unicyclic Graphs

作　　者：吴晓霞[1] 张莲珠[2] 覃城阜[3] 董哈微[4] 

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]厦门大学数学学院,福建厦门361005 [3]广西师范学院数学系,广西南宁530001 [4]闽江学院数学系,福建福州350108

出　　处：《数学研究》2013年第4期319-332,共14页Journal of Mathematical Study

基　　金：supported by NSFC(11171279,11101358);the NSF of Fujian(2012D140);the Scientific Research Fund of Fujian Provincial Education Department(JA12208,JA12266);the Scientific Research Foundation of Guangxi Education Committee(200103YB069);the Doctor Foundation of Minnan Normal University(201008)

摘　　要：研究图上Abelian沙堆模型问题.首先给出关于沙堆模型常返构型的极大雪崩序列,然后刻画了一些雪崩性质.基于这些性质,我们确定了单圈图的基本雪崩中每个顶点的topplings数及它的雪崩多项式,推广了R.Cori的结果.We first give a definition of a maximal avalanche sequence for a configuration of the Abelian sandpile model and characterize some avalanche properties. Applying these properties to unicyclic graphs, we determine their number of topplings on each vertex in principal avalanches and avalanche polynomials of the Abelian sandpile model, which generalizes R. Cori＇s results on cycles.

关 键 词：沙堆模型 常返构型 雪崩大小 

分 类 号：O157.5[理学—数学]