Recursion formulas for mixed moments of three fundamental random matrix ensembles are derived. The reason such recursive formulas are possible is closely related to properties of polygon gluings studied by Akhmedov and Shakirov. The proofs of the formulas are however written in such a way that they do not rely on such polygon-models and can be understood without a background in combinatorics.

翻译：推导了三种基本随机矩阵系综混合矩的递推公式。此类递推公式成立的原因与Akhmedov和Shakirov研究的多边形粘合性质密切相关。然而，公式的证明以不依赖此类多边形模型的方式编写，且无需组合学背景即可理解。