{"paper":{"title":"Hereditarily rigid relations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Karsten Sch\\\"olzel, Lucien Haddad, Maurice Pouzet, Miguel Couceiro","submitted_at":"2015-05-11T16:20:58Z","abstract_excerpt":"An $h$-ary relation $\\r$ on a finite set $A$ is said to be \\emph{hereditarily rigid} if the unary partial functions on $A$ that preserve $\\r$ are the subfunctions of the identity map or of constant maps. A family of relations ${\\mathcal F}$ is said to be \\emph{hereditarily strongly rigid} if the partial functions on $A$ that preserve every $\\r \\in {\\mathcal F}$ are the subfunctions of projections or constant functions. In this paper we show that hereditarily rigid relations exist and we give a lower bound on their arities. We also prove that no finite hereditarily strongly rigid families of re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02691","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"}