{"paper":{"title":"Unique inclusions of maximal C-clones in maximal clones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Edith Vargas-Garc\\'ia, Mike Behrisch","submitted_at":"2014-06-24T19:27:54Z","abstract_excerpt":"$\\mathit{C}$-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in [Creignou et al. 2008]. We completely describe the relationship w.r.t. set inclusion between maximal $\\mathit{C}$-clones and maximal clones. As a main result we obtain that for every maximal $\\mathit{C}$-clone there exists exactly one maximal clone in which it is contained. A precise description of this unique maximal clone, as well as a corresponding completeness criterion for $\\mathit{C}$-clones i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6344","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"}