{"paper":{"title":"Pairwise Suitable Family of Permutations and Boxicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Deepak Rajendraprasad, L. Sunil Chandran, Manu Basavaraju, Rogers Mathew","submitted_at":"2012-12-30T17:52:44Z","abstract_excerpt":"A family F of permutations of the vertices of a hypergraph H is called \"pairwise suitable\" for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the \"separation dimension\" of H and is denoted by \\pi(H). Equivalently, \\pi(H) is the smallest natural number k so that the vertices of H can be embedded in R^k such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6756","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"}