PreprintarXiv licencearXiv
Remarks on DAG exchangeability and generalized wreath products
Abstract
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.
Related
- Generalized free wreath products and their operator algebras
- Homological finiteness properties of wreath products
- Representation zeta functions of wreath products with finite groups
- Nonsofic wreath products of residually finite groups
- Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups
BibTeX
@misc{jung2026remarks,
title = {{Remarks on DAG exchangeability and generalized wreath products}},
author = {Paul Jung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34067},
eprint = {2609.34067},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34067},
}
RIS
TY - UNPB
TI - Remarks on DAG exchangeability and generalized wreath products
AU - Paul Jung
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34067
UR - https://arxiv.org/abs/2609.34067
AB - 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.
ER -