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The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW] as a class of elements of the symmetric group whose Kazhdan-Lusztig, Poincare polynomials, and the singular loci of whose Schubert varieties have fairly simple formulas and descriptions. Stankova and West [SW] gave an exact enumeration in terms of linear recurrences with const"},"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":"math/0207192","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2002-07-22T13:12:05Z","cross_cats_sorted":[],"title_canon_sha256":"bc12c62354b052a72817e435fa8a54741a8c8b96c6256bce82e252ea344b3d23","abstract_canon_sha256":"ba391efc1a45bb81d7cca0b2241fbf056b9e8626339bfcaa13ac0c3acab74329"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.448155Z","signature_b64":"cvJHdQghjKByEUG+GDwjhq3aUZY99l0Gk3veMhIaoejeEz4HujcD9e447oQD04V/XHzu40RdAcE0PnZ2ZNQdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f5feaed2cc78cb6e123a9fad32c872b8b980fbed169b68a3caf10224e6d786b","last_reissued_at":"2026-05-18T01:05:29.447746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.447746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"321-polygon-avoiding permutations and Chebyshev polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"T. 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