{"paper":{"title":"Ranks and presentations of some normally ordered inverse semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Rita Caneco, Teresa M. Quinteiro, V\\'itor H. Fernandes","submitted_at":"2019-05-27T20:29:51Z","abstract_excerpt":"In this paper we compute the rank and exhibit a presentation for the monoids of all $P$-stable and $P$-order preserving partial permutations on a finite set $\\Omega$, with $P$ an ordered uniform partition of $\\Omega$. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups ${\\sf NO}$ of all normally ordered (finite) inverse semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11489","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"}