Dimers, tilings and trees
Dimers, tilings and trees
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DOI：
10.1016/j.jctb.2004.07.001
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发表时间：
2004-11-01
影响因子：
1.4
通讯作者：
Sheffield, S
中科院分区：
文献类型：
--
作者：
Kenyon, RW;Sheffield, S
推广Temperley（伦敦数学学会讲义系列13（1974）202）、布鲁克斯等人（杜克数学杂志7（1940）312）和其他人（电子杂志Combin. 7（2000年）; Israel J.Math.105（1998）61），我们描述了三个平面对象之间的自然等价：加权二分平面图;平面马尔可夫链;和具有凸多边形的文件。这个等价性提供了一个加权二分平面图的二聚体覆盖和相应马尔可夫链的生成树之间的保测度双射。的filings对应于调和函数的马尔可夫链和“离散解析函数”的二分图。等价扩展到无限周期图，我们分类的“几乎周期”tilings和调和函数。(C)2004年由Elsevier Inc.出版
Generalizing results of Temperley (London Mathematical Society Lecture Notes Series 13 (1974) 202), Brooks et al. (Duke Math. J. 7 (1940) 312) and others (Electron. J. Combin. 7 (2000); Israel J. Math. 105 (1998) 61) we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; planar Markov chains; and filings with convex polygons. This equivalence provides a measure-preserving bijection between dimer coverings of a weighted bipartite planar graph and spanning trees of the corresponding Markov chain. The filings correspond to harmonic functions on the Markov chain and to "discrete analytic functions" on the bipartite graph.The equivalence is extended to infinite periodic graphs, and we classify the resulting "almost periodic" tilings and harmonic functions. (C) 2004 Published by Elsevier Inc.