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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 -"},"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":"q-alg/9710025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-10-21T07:48:59Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"e53c3cd7718f122a639939b9fe144b9954de491f3a29f1c2a431cc9247554e1f","abstract_canon_sha256":"978ce26fe0523e69eb3c31f151aac23532257e39dbe27899b8867c4988d15fe2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:07.220960Z","signature_b64":"HFxoXYOcGnal5iFFb7/uIUhL+EVWc2vUzi7Zuk5ShwUfcCIP+gRL8VIbbq2/dr1uVEwvKZBq4aRXJ8tnxrFCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"676e2f7b17318980ace8c3ee1f06929a8238907e8da703a66fefca232b3458dc","last_reissued_at":"2026-05-18T01:05:07.220260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:07.220260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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