Alternating-Sign Matrices and Domino Tilings (Part II)
Alternating-Sign Matrices and Domino Tilings (Part II)
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交替符号矩阵和多米诺骨牌（第二部分）
DOI：
10.1023/a:1022483817303
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发表时间：
1992
影响因子：
0.8
通讯作者：
J. Propp
中科院分区：
文献类型：
--
作者：
N. Elkies;G. Kuperberg;M. Larsen;J. Propp
我们继续研究在我们之前的文章中被称为阿兹特克钻石的平面区域家族，并研究这些区域可以被多米诺骨牌平铺的方式。给出了主公式的两个证明。第一种方法使用GL（n）的表示理论。第二个是更具组合性，并产生一个生成函数，不仅给出了数量的多米诺骨牌平铺的阿兹特克钻石的顺序n，但也信息的方向多米诺骨牌（垂直与水平）和访问一个平铺从另一个通过本地修改。最后，我们探讨了本文研究的组合对象和Lieb研究的方形冰模型之间的联系。
We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.