{"paper":{"title":"An Asymmetric Random Rado Theorem: 1-statement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elad Aigner-Horev, Yury Person","submitted_at":"2019-06-13T11:46:46Z","abstract_excerpt":"A classical result by Rado characterises the so-called partition-regular matrices $A$, i.e.\\ those matrices $A$ for which any finite colouring of the positive integers yields a monochromatic solution to the equation $Ax=0$. We study the {\\sl asymmetric} random Rado problem for the (binomial) random set $[n]_p$ in which one seeks to determine the threshold for the property that any $r$-colouring, $r \\geq 2$, of the random set has a colour $i \\in [r]$ admitting a solution for the matrical equation $A_i x = 0$, where $A_1,\\ldots,A_r$ are predetermined partition-regular matrices pre-assigned to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05614","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"}