阿兹特克钻石的非对角线对称多米诺骨牌瓷砖

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-11-03 DOI:10.37236/11921

Yi-Lin Lee

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引用次数: 0

摘要

在Kuperberg于2002年提出的非对角线对称交替符号矩阵的启发下，我们引入了阿兹特克钻石多米诺骨牌的一个新的对称类，称为非对角线对称类。我们使用不相交点阵路径的方法和对Stembridge的非相交点阵路径族的Pfaffian公式的修改来枚举我们的新对称类。阿兹特克钻石的非对角线对称多米诺骨牌瓷砖的数目可以表示为一个矩阵的普氏矩阵，该矩阵的元素满足一个简单的递归关系。

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Off-Diagonally Symmetric Domino Tilings of the Aztec Diamond

We introduce a new symmetry class of domino tilings of the Aztec diamond, called the off-diagonal symmetry class, which is motivated by the off-diagonally symmetric alternating sign matrices introduced by Kuperberg in 2002. We use the method of non-intersecting lattice paths and a modification of Stembridge's Pfaffian formula for families of non-intersecting lattice paths to enumerate our new symmetry class. The number of off-diagonally symmetric domino tilings of the Aztec diamond can be expressed as a Pfaffian of a matrix whose entries satisfy a nice and simple recurrence relation.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.