{"paper":{"title":"Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. D. Adeshola, A. Umar","submitted_at":"2013-03-29T15:54:22Z","abstract_excerpt":"Let ${\\cal T}_n$ be the full symmetric semigroup on $X_n = \\{1, 2,..., n\\}$ and let ${\\cal OCT}_n$ and ${\\cal ORCT}_n$ be its subsemigroups of order-preserving and order-preserving or order-reversing full contraction mappings of $X_n$, respectively. In this paper we investigate the cardinalities of some equivalences on ${\\cal OCT}_n$ and ${\\cal ORCT}_n$ which lead naturally to obtaining the orders of these subsemigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7428","kind":"arxiv","version":2},"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"}