In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a byproduct, we also find such a formula for the unrestricted case as well. Our proofs rely on a new technique for counting the number of perfect matchings of graphs, proposed by the authors recently.

翻译：本文通过归纳求和公式，计算了阿兹特克钻石的对角线对称、以及对角线兼反对角线对称的多米诺骨牌覆盖方案数。作为推论，我们也给出了无约束情况下的相应公式。我们的证明依赖于作者近期提出的一种计算图完美匹配数的新技术。