{"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\\} $. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09365","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}