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This answers a question of Barto\\v{s}ov\\'{a} and Kwiatkowska. We also prove a common generalization of such a result and the Galvin--Glazer--Hindman theorem on finite products, in the setting of layered partial semigroups in"},"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":"1603.09365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T20:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"6efc803ffdb2f6422a0c919a6d28c6ce2fa1bb99be38359bad47648909ca13eb","abstract_canon_sha256":"dd52d4480f94b6328149e6db65f39cd13ebf8fd2ae0416a98ce1922a6f67e5db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:31.357766Z","signature_b64":"OZFkDC264s3S8co0sPKFZUBOKttGKhJRkUS/NZ2otLLFmLxf1QCWsXF/3huJNncWCTw7weVr2WZuwT50EyqZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d1445b7c388212f73d9c6d05ad78c99aa5fccfbb384f81c0f6c40d070502711","last_reissued_at":"2026-05-18T00:38:31.357061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:31.357061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gowers' Ramsey theorem for generalized tetris operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Martino Lupini","submitted_at":"2016-03-30T20:21:54Z","abstract_excerpt":"We prove a generalization of Gowers' theorem for $\\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\\mathrm{FIN}_{k}\\rightarrow \\mathrm{FIN}_{k-1}$, one considers all maps from $\\mathrm{FIN}_{k}$ to $\\mathrm{FIN}_{j}$ for $0\\leq j\\leq k$ arising from nondecreasing surjections $f:\\left\\{ 0,1,\\ldots ,k+1\\right\\} \\rightarrow \\left\\{ 0,1,\\ldots ,j+1\\right\\} $. 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