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One of them, $V_0(\\boldsymbol A)$ with mean $\\mu$, gives the total number of solutions for a generalised birthday problem, and the other, $W(\\boldsymbol A)$ with mean $\\lambda$, gives the number of solutions detected by Wagner's tree based algorithm.\n  We establish two limit theorems. Theorem 2.1 describes an asymptotical behaviour of the ratio $\\lambda/\\mu$ as $M\\to\\infty$. Theorem 2.2 suggests Chen-Stein bounds for the"},"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":"1507.05490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-20T13:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"87a6e876816c80556ce58b2abaaaff9a29b2a7994404c795a4a42701a78cd389","abstract_canon_sha256":"16c2a88e9b6c18f7cce7b62a05edfeb2cadf1ca638453078592377fed686c3d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:36.672034Z","signature_b64":"bbvYE4LShG2Lvpx0M82ONdWK8kURu7G0bYfBxvEEXprqReA9zLBUpuU1LA6pAJg6h+iqRvcU9ZBEYlfU0qB+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"640186c036f08d30bd3b71d97804057e78e3dcecbcc2d617abeb34c72b49009e","last_reissued_at":"2026-05-18T01:36:36.671412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:36.671412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic results for the number of Wagner's solutions to a generalised birthday problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexey Lindo, Serik Sagitov","submitted_at":"2015-07-20T13:41:31Z","abstract_excerpt":"We study two functionals of a random matrix $\\boldsymbol A$ with independent elements uniformly distributed over the cyclic group of integers $\\{0,1,\\ldots, M-1\\}$ modulo $M$. One of them, $V_0(\\boldsymbol A)$ with mean $\\mu$, gives the total number of solutions for a generalised birthday problem, and the other, $W(\\boldsymbol A)$ with mean $\\lambda$, gives the number of solutions detected by Wagner's tree based algorithm.\n  We establish two limit theorems. Theorem 2.1 describes an asymptotical behaviour of the ratio $\\lambda/\\mu$ as $M\\to\\infty$. 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