{"paper":{"title":"Hultman Numbers and Generalized Commuting Probability in Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.GR","authors_text":"Avraham Goldstein, Robert Shwartz, Vadim E. Levit, Yonah Cherniavsky","submitted_at":"2014-03-16T01:20:14Z","abstract_excerpt":"Let $G$ be a finite group and $\\pi$ be a permutation from $S_{n}$.\n  We investigate the distribution of the probabilities of the equality \\[ a_{1}a_{2}\\cdots a_{n-1}a_{n}=a_{\\pi_{1}}a_{\\pi_{2}}\\cdots a_{\\pi_{n-1}}a_{\\pi_{n}} \\] when $\\pi$ varies over all the permutations in $S_{n}$.\n  The probability \\[ Pr_{\\pi}(G)=Pr(a_{1}a_{2}\\cdots a_{n-1}a_{n}=a_{\\pi_{1}}a_{\\pi_{2}}\\cdots a_{\\pi_{n-1}}a_{\\pi_{n}}) \\] is identical to $Pr_{1}^{\\omega}(G)$, with \\[ \\omega=a_{1}a_{2}...a_{n-1}a_{n}a_{\\pi_{1}}^{-1}a_{\\pi_{2}}^{-1}\\cdots a_{\\pi_{n-1}}^{-1}a_{\\pi_{n}}^{-1}, \\] as it is defined in \\cite{DasNath1} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3868","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"}