{"paper":{"title":"Extremal $t$-intersecting Families of Permutations for Large $t$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pitchayut Saengrungkongka","submitted_at":"2026-05-25T17:12:19Z","abstract_excerpt":"A set of permutations of $\\{1,2,\\dots,n\\}$ is $t$-intersecting if any two permutations agree on at least $t$ inputs. A recent work by Kupavskii, in the spirit of the Erd\\H{o}s-Ko-Rado Theorem, shows that for all $t\\leq n-O\\left(\\frac{n\\log\\log n}{\\log n}\\right)$, every $t$-intersecting family of permutations of $\\{1,2,\\dots,n\\}$ with the maximum size must be isomorphic to the set $$A_k = \\{\\sigma : \\sigma(i)=i\\text{ for at least } t+k \\text{ indices } i\\in\\{1,2,\\dots,t+2k\\}\\}$$ for some $k$. By refining Kupavskii's spread approximation technique, we prove that this conclusion holds for a wider"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}