{"paper":{"title":"Low-degree Boolean functions on $S_n$, with an application to isoperimetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Ellis, Ehud Friedgut, Yuval Filmus","submitted_at":"2015-11-27T14:51:32Z","abstract_excerpt":"We prove that Boolean functions on $S_n$, whose Fourier transform is highly concentrated on irreducible representations indexed by partitions of $n$ whose largest part has size at least $n-t$, are close to being unions of cosets of stabilizers of $t$-tuples. We also obtain an edge-isoperimetric inequality for the transposition graph on $S_n$ which is asymptotically sharp for subsets of $S_n$ of size $n!/\\textrm{poly}(n)$, using eigenvalue techniques. We then combine these two results to obtain a sharp edge-isoperimetric inequality for subsets of $S_n$ of size $(n-t)!$, where $n$ is large compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08694","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"}