{"paper":{"title":"The rank of the semigroup of transformations stabilising a partition of a finite set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Csaba Schneider, J. D. Mitchell, Joao Araujo, Wolfram Bentz","submitted_at":"2014-04-06T16:48:06Z","abstract_excerpt":"Let $\\mathcal{P}$ be a partition of a finite set $X$. We say that a full transformation $f:X\\to X$ preserves (or stabilizes) the partition $\\mathcal{P}$ if for all $P\\in \\mathcal{P}$ there exists $Q\\in \\mathcal{P}$ such that $Pf\\subseteq Q$. Let $T(X,\\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\\mathcal{P}$.\n  In 2005 Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\\mathcal{P})$, when $\\mathcal{P}$ is a partition in which all of its parts have the same size. In addition, Huisheng conjectured that his bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1598","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"}