{"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 $M\\to\\infty$. Theorem 2.2 suggests Chen-Stein bounds for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05490","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"}