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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} "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.3868","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-16T01:20:14Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"578a12320e00f0c5d217ffbf979998d2d9cbfc4ea47adac02b9a283191b964bf","abstract_canon_sha256":"f95481fb1634afae5b83bff82d7c172bb9bb8f1a532b09b7fc2ce84bec829f94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:16.973662Z","signature_b64":"cWntnDo83hb14aclh5ixeEncPG8PWSQ53oIGtMQwrS3MfF5s/3f8UVeUDgGMN5fK0+tXl6Dm2TyxgRHptp26AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d2e1e7f06ace793cf56150b4a5880730a1644266a1af49817dde361f19ca0b9","last_reissued_at":"2026-05-18T02:41:16.972971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:16.972971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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