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Propp and Roby defined the triple $(X, G, \\xi)$ to be \\emph{homomesic} if for any orbits $\\mathcal{O}_1, \\mathcal{O}_2$, the average value of the statistic $\\xi$ is the same, that is \\[\\frac{1}{{|\\mathcal{O}_1|}}\\sum_{x \\in \\mathcal{O}_1} \\xi(x) = \\frac{1}{|\\mathcal{O}_2|}\\sum_{y \\in \\mathcal{O}_2} \\xi(y).\\]\n  In 2013 Propp and Roby conjectured the following instance of homomesy. Let $\\mathrm{SSYT}_k(m \\times n)$ denote the set of semistandard Young tableaux o"},"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":"1308.0546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T15:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"5fcd8981d4160c6f669d477a6c72d826eb2df25370bb895828d51b0474f1ef7b","abstract_canon_sha256":"8283d986de10f533f7f6ac027a0ed68d216878d0d7139e64127d0933446fbdb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.394833Z","signature_b64":"bdT9SzLMJe4Bh9Hpa/QyDgoUWRTMte6AIS7ao3swXXqno9zo1Mu28plRPFiWP9XyV3947Wmbk9BrvuU+MfxYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a376cf8a5e3923e9330dc8617e0636037e71b7860e6393eb3547aa55b753a93e","last_reissued_at":"2026-05-18T00:13:38.394258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.394258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proofs and generalizations of a homomesy conjecture of Propp and Roby","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Saracino, Jonathan Bloom, Oliver Pechenik","submitted_at":"2013-08-02T15:54:42Z","abstract_excerpt":"Let $G$ be a group acting on a set $X$ of combinatorial objects, with finite orbits, and consider a statistic $\\xi : X \\to \\mathbb{C}$. 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