关于DAG可交换性与广义圈积的注记
Remarks on DAG exchangeability and generalized wreath products
- Fordham University（福特汉姆大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文指出DAG可交换性定义中的群恰为广义圈积，并重述表示定理，给出块矩阵可交换性的具体表示。
AI中文摘要：
受各种标准统计数组结构的启发，Bailey、Praeger、Rowley和Speed（1983）将偏序集块结构的自同构群描述为广义圈积。我们观察到，这些正是Jung、Lee、Staton和Yang（2021）中用于定义DAG可交换性的群，并以后者的语言重述了其表示定理。作为一个具体例子，我们写出了块行和块列分别可交换、且每块内行和列也可独立置换的块矩阵的相应表示。
英文摘要：
Motivated by the structure of various standard statistical arrays, Bailey, Praeger, Rowley and Speed (1983) described the automorphism groups of poset block structures as generalized wreath products. We observe that these are exactly the groups used to define DAG exchangeability in Jung, Lee, Staton and Yang (2021), and we restate the representation theorem of the latter work in this language. As a concrete example, we write out the resulting representation for block matrices whose block rows and block columns are separately exchangeable, and whose rows and columns may also be permuted independently inside each block.
