{"paper":{"title":"The 3-way intersection problem for S(2, 4, v) designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nasrin Soltankhah, Saeedeh Rashidi","submitted_at":"2013-01-21T06:36:46Z","abstract_excerpt":"In this paper the 3-way intersection problem for $S(2,4,v)$ designs is investigated. Let $b_{v}=\\frac {v(v-1)}{12}$ and $I_{3}[v]=\\{0,1,...,b_{v}\\}\\setminus\\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\\}$. Let $J_{3}[v]=\\{k|$ there exist three $S(2,4,v)$ designs with $k$ same common blocks$\\}$. We show that $J_{3}[v]\\subseteq I_{3}[v]$ for any positive integer $v\\equiv1, 4\\ (\\rm mod \\ 12)$ and $J_{3}[v]=I_{3}[v]$, for $ v\\geq49$ and $v=13 $. We find $J_{3}[16]$ completely. Also we determine some values of $J_{3}[v]$ for $\\ v=25,28,37$ and 40."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4764","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"}