{"paper":{"title":"On $t$-Intersecting Families of Permutations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dor Minzer, Nathan Keller, Noam Lifshitz, Ohad Sheinfeld","submitted_at":"2023-03-28T06:30:07Z","abstract_excerpt":"We prove that there exists a constant $c_0$ such that for any $t \\in \\mathbb{N}$ and any $n\\geq c_0 t$, if $A \\subset S_n$ is a $t$-intersecting family of permutations then$|A|\\leq (n-t)!$. Furthermore, if $|A|\\ge 0.75(n-t)!$ then there exist $i_1,\\ldots,i_t$ and $j_1,\\ldots,j_t$ such that $\\sigma(i_1)=j_1,\\ldots,\\sigma(i_t)=j_t$ holds for any $\\sigma \\in A$. This shows that the conjectures of Deza and Frankl (1977) and of Cameron (1988) on $t$-intersecting families of permutations hold for all $t \\leq c_0 n$. Our proof method, based on hypercontractivity for global functions, does not use the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.15755","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.15755/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"}