{"paper":{"title":"Homogeneous Dual Ramsey Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Jose G. Mijares","submitted_at":"2019-07-05T04:34:00Z","abstract_excerpt":"For positive integers $k < n$ such that $k$ divides $n$, let $(n)^k_{\\hom}$ be the set of homogeneous $k$-partitions of $\\{1, \\dots, n\\}$, that is, the set of partitions of $\\{1, \\dots, n\\}$ into $k$ classes of the same cardinality. In the article \"Ramsey properties of infinite measure algebras and topological dynamics of the group of measure preserving automorphisms: some results and an open problem\" by Kechris, Sokic, and Todorcevic, the following question was asked:\n  Is it true that given positive integers $k < m$ and $N$ such that $k$ divides $m$, there exists a number $n>m$ such that $m$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02675","kind":"arxiv","version":2},"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"}