{"paper":{"title":"Simple signed Steiner triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Ghorbani, G. B. Khosrovshahi","submitted_at":"2011-05-14T13:11:58Z","abstract_excerpt":"Let $X$ be a $v$-set, $\\B$ a set of 3-subsets (triples) of $X$, and $\\B^+\\cup\\B^-$ a partition of $\\B$ with $|\\B^-|=s$. The pair $(X,\\B)$ is called a simple signed Steiner triple system, denoted by ST$(v,s)$, if the number of occurrences of every 2-subset of $X$ in triples $B\\in\\B^+$ is one more than the number of occurrences in triples $B\\in\\B^-$. In this paper we prove that $\\st(v,s)$ exists if and only if $v\\equiv1,3\\pmod6$, $v\\ne7$, and $s\\in\\{0,1,...,s_v-6,s_v-4,s_v\\}$, where $s_v=v(v-1)(v-3)/12$ and for $v=7$, $s\\in\\{0,2,3,5,6,8,14\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2896","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"}