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We use this tool to show that there is no distance-regular graph with intersection array $\\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\\}$ ($r, t \\ge 1$), $\\{135, 128, 16; 1, 16, 120\\}$, $\\{234, 165, 12; 1, 30, 198\\}$ or $\\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are"},"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":"1803.10797","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-03-28T18:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"80c9090a7e6cfd06cccf40b54b7f3b61c7caa7c591e6b94b3584c01e938cdbba","abstract_canon_sha256":"9af209241482ceb0a0ac45d45c4c6130a7ffd4a5a79ffa942f2c25b56d3531e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:49.506795Z","signature_b64":"2RlV9w6i3/yqSECZoHnATX1nNJGeKo7Sgrp9P38gFGf85eXbBgh0wTU2r19QfPPgEJrjsTd+CzliRTDHjW+gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1882fca2f0672054295349b5ee27ef316954a1aafc54eaa12145bf04157cfbe6","last_reissued_at":"2026-05-18T00:02:49.506205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:49.506205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Using symbolic computation to prove nonexistence of distance-regular graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jano\\v{s} Vidali","submitted_at":"2018-03-28T18:40:59Z","abstract_excerpt":"A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array $\\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\\}$ ($r, t \\ge 1$), $\\{135, 128, 16; 1, 16, 120\\}$, $\\{234, 165, 12; 1, 30, 198\\}$ or $\\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. 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