{"paper":{"title":"A coding problem for pairs of subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bela Bollobas, G. O. H. Katona, Ida Kantor, Imre Leader, Zoltan Furedi","submitted_at":"2014-03-15T20:03:44Z","abstract_excerpt":"Let $X$ be an $n$--element finite set, $0<k\\leq n/2$ an integer. Suppose that $\\{A_1,A_2\\} $ and $\\{B_1,B_2\\} $ are pairs of disjoint $k$-element subsets of $X$ (that is, $|A_1|=|A_2|=|B_1|=|B_2|=k$, $A_1\\cap A_2=\\emptyset$, $B_1\\cap B_2=\\emptyset$). Define the distance of these pairs by $d(\\{A_1,A_2\\} ,\\{B_1,B_2\\})=\\min \\{|A_1-B_1|+|A_2-B_2|, |A_1-B_2|+|A_2-B_1|\\} $. This is the minimum number of elements of $A_1\\cup A_2$ one has to move to obtain the other pair $\\{B_1,B_2\\}$. Let $C(n,k,d)$ be the maximum size of a family of pairs of disjoint subsets, such that the distance of any two pairs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3847","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"}