{"paper":{"title":"On extendability of permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.GR","authors_text":"Mark Pankov","submitted_at":"2012-06-27T17:14:50Z","abstract_excerpt":"Let $V$ be a left vector space over a division ring and let ${\\mathcal P}(V)$ be the associated projective space. We describe all finite subsets $X\\subset V$ such that every permutation on $X$ can be extended to a linear automorphism of $V$ and all finite subsets ${\\mathcal X}\\subset {\\mathcal P}(V)$ such that every permutation on ${\\mathcal X}$ can be extended to an element of ${\\rm PGL}(V)$. Also, we reformulate the results in terms of linear and projective representations of symmetric groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6340","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"}