{"paper":{"title":"A Burge tree of Virasoro-type polynomial identities","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Australia.), Keith S. M. Lee, Omar Foda, Statistics, Trevor A. Welsh (Department of Mathematics, University of Melbourne","submitted_at":"1997-10-21T07:48:59Z","abstract_excerpt":"Using a summation formula due to Burge, and a combinatorial identity between partition pairs, we obtain an infinite tree of q-polynomial identities for the Virasoro characters \\chi^{p, p'}_{r, s}, dependent on two finite size parameters M and N, in the cases where:\n  (i) p and p' are coprime integers that satisfy 0 < p < p'.\n  (ii) If the pair (p', p) has a continued fraction (c_1, c_2, ... , c_{t-1}, c_t+2), where t >= 1, then the pair (s, r) has a continued fraction (c_1, c_2, ... , c_{u-1}, d), where 1 =< u =< t, and 1 =< d =< c_{u}.\n  The limit M -> infinity, for fixed N, and the limit N -"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9710025","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"}