{"paper":{"title":"The Determination of 2-color zero-sum generalized Schur Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aaron Robertson, Bidisha Roy, Subha Sarkar","submitted_at":"2018-03-02T14:23:44Z","abstract_excerpt":"Consider the equation $\\mathcal{E}: x_1+ \\cdots+x_{k-1} =x_{k}$ and let $k$ and $r$ be positive integers such that $r\\mid k$. The number $S_{\\mathfrak{z},2}(k;r)$ is defined to be the least positive integer $t$ such that for any 2-coloring $\\chi: [1, t] \\to \\{0, 1\\}$ there exists a solution $(\\hat{x}_1, \\hat{x}_2, \\ldots, \\hat{x}_k)$ to the equation $\\mathcal{E}$ satisfying $\\displaystyle \\sum_{i=1}^k\\chi(\\hat{x}_i) \\equiv 0\\pmod{r}$. In a recent paper, the first author posed the question of determining the exact value of $S_{\\mathfrak{z}, 2}(k;4)$. In this article, we solve this problem and s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00861","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"}