{"paper":{"title":"On the existence of 3-way k-homogeneous Latin trades","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Behrooz Bagheri Gh., Diane Donovan, E. S. Mahmoodian","submitted_at":"2012-07-09T07:21:14Z","abstract_excerpt":"A {\\sf $\\mu$-way Latin trade} of volume $s$ is a collection of $\\mu$ partial Latin squares $T_1,T_2,...,T_{\\mu}$, containing exactly the same $s$ filled cells, such that if cell $(i, j)$ is filled, it contains a different entry in each of the $\\mu$ partial Latin squares, and such that row $i$ in each of the $\\mu$ partial Latin squares contains, set-wise, the same symbols and column $j$, likewise. %If $\\mu=2$, $(T_1,T_2)$ is called a {\\sf Latin bitrade}. It is called {\\sf $\\mu$-way $k$-homogeneous Latin trade}, if in each row and each column $T_r$, for $1\\le r\\le \\mu,$ contains exactly $k$ elem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1969","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"}