{"paper":{"title":"Eigenvalue Fluctuations of Symmetric Group Permutation Representations on k-tuples and k-subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benjamin Tsou","submitted_at":"2018-10-28T23:38:04Z","abstract_excerpt":"Let the term $k$-representation refer to the permutation representations of the symmetric group $\\mathfrak{S}_n$ on $k$-tuples and $k$-subsets as well as the $S^{(n-k,1^k)}$ irreducible representation of $\\mathfrak{S}_n$. Endow $\\mathfrak{S}_n$ with the Ewens distribution and let $\\alpha$ and $\\beta$ be linearly independent irrational numbers over $\\mathbb{Q}$. Then for fixed $k > 1$ we show that as $n \\to \\infty$, the normalized count of the number of eigenangles in a fixed interval $(\\alpha, \\beta)$ of a $k$-representation evaluated at a random element $\\sigma \\in \\mathfrak{S}_n$ converges w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11904","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"}