{"paper":{"title":"On Disjoint Golomb Rulers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Changjun Fan, Meilian Liang, Xiu Baoxin","submitted_at":"2014-05-18T18:30:57Z","abstract_excerpt":"A set $\\{a_i\\:|\\: 1\\leq i \\leq k\\}$ of non-negative integers is a Golomb ruler if differences $a_i-a_j$, for any $i \\neq j$, are all distinct. A set of $I$ disjoint Golomb rulers (DGR) each being a $J$-subset of $\\{1,2,\\cdots, n\\}$ is called an $(I,J,n)-DGR$. Let $H(I, J)$ be the least positive $n$ such that there is an $(I,J,n)-DGR$. In this paper, we propose a series of conjectures on the constructions and structures of DGR. The main conjecture states that if $A$ is any set of positive integers such that $|A| = H(I, J)$, then there are $I$ disjoint Golomb rulers, each being a $J$-subset of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4535","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"}