{"paper":{"title":"On the possible volume of $\\mu$-$(v,k,t)$ trades","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nasrin Soltankhah, Saeedeh Rashidi","submitted_at":"2013-10-29T11:18:01Z","abstract_excerpt":"A $\\mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $\\mu$ disjoint collections $T_1$, $T_2, \\dots T_{\\mu}$, each of $m$ blocks, such that for every $t$-subset of $v$-set $V$ the number of blocks containing this t-subset is the same in each $T_i\\ (1\\leq i\\leq \\mu)$. In other words any pair of collections $\\{T_i,T_j\\}$, $1\\leq i<j \\leq \\mu$ is a $(v,k,t)$ trade of volume $m$.\n  In this paper we investigate the existence of $\\mu$-way $(v,k,t)$ trades and also we prove the existence of: (i)~3-way $(v,k,1)$ trades (Steiner trades) of each volume $m,m\\geq2$. (ii) 3-way $(v,k,2)$ trades of each v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7759","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"}