{"paper":{"title":"Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdollah Khodkar, Diane Donovan, Fatih Demirkale","submitted_at":"2014-01-30T15:47:21Z","abstract_excerpt":"Two Latin squares $L=[l(i,j)]$ and $M=[m(i,j)]$, of even order $n$ with entries $\\{0,1,2,\\ldots,n-1\\}$, are said to be nearly orthogonal if the superimposition of $L$ on $M$ yields an $n\\times n$ array $A=[(l(i,j),m(i,j))]$ in which each ordered pair $(x,y)$, $0\\leq x,y\\leq n-1$ and $x\\neq y$, occurs at least once and the ordered pair $(x,x+n/2)$ occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders $48k+14$, $48k+22$, $48k+38$ and $48k+46$. The techniques employed are based on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7889","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"}