{"paper":{"title":"An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Dimitri Polyakov","submitted_at":"2017-02-15T14:45:22Z","abstract_excerpt":"We study the correlators of irregular vertex operators in two-dimensional conformal field theory (CFT) in order to propose an exact analytic formula for calculating numbers of partitions, that is:\n  1) for given $N,k$, finding the total number $\\lambda(N|k)$ of length $k$ partitions of $N$: $N=n_1+...+n_k;0<n_1\\leq{n_2}...\\leq{n_k}$.\n  2) finding the total number $\\lambda(N)=\\sum_{k=1}^N\\lambda(N|k)$ of partitions of a natural number $N$\n  We propose an exact analytic expression for $\\lambda(N|k)$ by relating two-point short-distance correlation functions of irregular vertex operators in $c=1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04631","kind":"arxiv","version":3},"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"}