{"author":[{"orcid":"0009-0009-7736-4885","full_name":"Klawuhn, Lukas-André Dominik","last_name":"Klawuhn","first_name":"Lukas-André Dominik","id":"91965"},{"full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe","last_name":"Schmidt"}],"language":[{"iso":"eng"}],"date_updated":"2024-11-15T12:34:03Z","abstract":[{"text":"It is known that the notion of a transitive subgroup of a permutation group\r\n$P$ extends naturally to the subsets of $P$. We study transitive subsets of the\r\nwreath product $G \\wr S_n$, where $G$ is a finite abelian group. This includes\r\nthe hyperoctahedral group for $G=C_2$. We give structural characterisations of\r\ntransitive subsets using the character theory of $G \\wr S_n$ and interpret such\r\nsubsets as designs in the conjugacy class association scheme of $G \\wr S_n$. In\r\nparticular, we prove a generalisation of the Livingstone-Wagner theorem and\r\ngive explicit constructions of transitive sets. Moreover, we establish\r\nconnections to orthogonal polynomials, namely the Charlier polynomials, and use\r\nthem to study codes and designs in $C_r \\wr S_n$. Many of our results extend\r\nresults about the symmetric group $S_n$.","lang":"eng"}],"status":"public","page":"38","year":"2024","_id":"56429","type":"preprint","external_id":{"arxiv":["2409.20495"]},"date_created":"2024-10-08T13:14:45Z","publication":"arXiv:2409.20495","department":[{"_id":"100"}],"title":"Transitivity in wreath products with symmetric groups","citation":{"ama":"Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups. <i>arXiv:240920495</i>. Published online 2024.","short":"L.-A.D. Klawuhn, K.-U. Schmidt, ArXiv:2409.20495 (2024).","apa":"Klawuhn, L.-A. D., &#38; Schmidt, K.-U. (2024). Transitivity in wreath products with symmetric groups. In <i>arXiv:2409.20495</i>.","ieee":"L.-A. D. Klawuhn and K.-U. Schmidt, “Transitivity in wreath products with symmetric groups,” <i>arXiv:2409.20495</i>. 2024.","bibtex":"@article{Klawuhn_Schmidt_2024, title={Transitivity in wreath products with symmetric groups}, journal={arXiv:2409.20495}, author={Klawuhn, Lukas-André Dominik and Schmidt, Kai-Uwe}, year={2024} }","mla":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024.","chicago":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024."},"user_id":"91965"}