{"paper":{"title":"The Classification of Partition Homogeneous Groups with Applications to Semigroup Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jo\\~ao Ara\\'ujo, Jorge Andr\\'e, Peter J. Cameron","submitted_at":"2013-04-27T17:55:21Z","abstract_excerpt":"Let $\\lambda=(\\lambda_1,\\lambda_2,...)$ be a \\emph{partition} of $n$, a sequence of positive integers in non-increasing order with sum $n$. Let $\\Omega:=\\{1,...,n\\}$. An ordered partition $P=(A_1,A_2,...)$ of $\\Omega$ has \\emph{type} $\\lambda$ if $|A_i|=\\lambda_i$.\n  Following Martin and Sagan, we say that $G$ is \\emph{$\\lambda$-transitive} if, for any two ordered partitions $P=(A_1,A_2,...)$ and $Q=(B_1,B_2,...)$ of $\\Omega$ of type $\\lambda$, there exists $g\\in G$ with $A_ig=B_i$ for all $i$. A group $G$ is said to be \\emph{$\\lambda$-homogeneous} if, given two ordered partitions $P$ and $Q$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7391","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}