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We noted (and proved) that when M is the shape with n cells consisting of 3 followed by n-3 ones, the former sum equals one half time the analogous sum over hook shapes with n+2 cells and M is the partition consisting of 3,2, followed by n-3 ones.\n  Here we show that"},"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":"1510.07061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-23T20:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"e9cffaca1b128a3ed2a845e45017f0780825c9771fd6f3004d070af85a50ec38","abstract_canon_sha256":"ef4bcc098a73618eca7c7316277a3f44832700b7c262d5d005bd569c0271218e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:20.224250Z","signature_b64":"A4TAG45XwMRGu70vLjn3iS4s8eczsH3rsX2ly3ALH0ay7lEvjWz47D5eVyMKzhQPn5DeKZ1pL0vCvjKIA8asBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c6f959e66e340127d96f7c9f3000392a57ce0fa85f1872e457d816bb6caaf2d","last_reissued_at":"2026-05-18T01:29:20.223670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:20.223670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surprising Relations Between Sums-Of-Squares of Characters of the Symmetric Group Over Two-Rowed Shapes and Over Hook Shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amitai Regev, Doron Zeilberger","submitted_at":"2015-10-23T20:37:59Z","abstract_excerpt":"In a recent article (arXiv:1507.03499) (joint with Alon Regev) we studied sums of squares of characters Chi(L,M) of the Symmetric Group over shapes L that are two-rowed, and shapes L that are hook shapes, and M is an arbitrary shape that mostly consists of ones, and designed algorithms for closed-form evaluations of each of these. 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