{"paper":{"title":"Smallest defining sets of super-simple 2 - (v, 4,1) directed designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Farzane Amirzade, Nasrin Soltankhah","submitted_at":"2012-05-29T15:33:53Z","abstract_excerpt":"A $2-(v,k,\\lambda)$ directed design (or simply a $2-(v,k,\\lambda)DD$) is super-simple if its underlying $2-(v,k,2\\lambda)BIBD$ is super-simple, that is, any two blocks of the $BIBD$ intersect in at most two points. A $2-(v,k,\\lambda)DD$ is simple if its underlying $2-(v,k,2\\lambda)BIBD$ is simple, that is, it has no repeated blocks.\n  A set of blocks which is a subset of a unique $2-(v,k,\\lambda)DD$ is said to be a defining set of the directed design. A smallest defining set, is a defining set which has smallest cardinality. In this paper simultaneously we show that the necessary and sufficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6395","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"}