关于不完全r-自正交拉丁方的存在性

Study on Existence of Incomplete r-self-orthogonal Latin Squares

如果2个n阶不完全拉丁方重叠后正好产生r个不同的有序对,则称它们是r-正交的,记作r-IMOLS(n,u),其中u为缺少的子拉丁方的阶数.进一步,如果第2个拉丁方是第1个拉丁方的转置,则称它们是r-自正交的,记作r-ISOLS(n,u).本文给出当u∈{1,2,3,4}时,r-ISOLS(4m+u,u)的存在性。

Two incomplete Latin squares of order v are r -orthogonal if their superposition produces exactly r distinct ordered pairs, denoted by r-IMOLS （n, u）, where u is the order of holey Latin square. In addition, if the second square is the transpose of the first one, then the first square is deemed to be r -self-orthogonal, denoted by r -ISOLS （n,u）. In this paper, the existence ofr -ISOLS （4m ＋ u,u） is investigated for the case u ∈ {1,2,3,4}.