【摘要】 2个v阶拉丁方,L=(lij)和M=(mij)被称为是r-正交的,如果把它们重叠起来可以得到恰好r个不同的有序元素偶,即{(lij,mij):1≤i,j≤v}=r,记为r-MOLS(v).r-MOLS(v)在r∈{v+1,v2-1}上的不存在性已经得到证明.如果M是L的(3,2,1)-共轭,可认为L是(3,2,1)-共轭r-正交的,可记为(3,2,1)-r-COLS(v).并且证明了(3,2,1)-r-COLS(v)在r∈{v+2,v+3,v+5}上的不存在性.更多还原

【Abstract】 Two latin squares of order v,L =(lij) and M =(mij) are called to be r-orthogonal if their superposition produces exactly r distinct ordered pairs,that is {(lij,mij) :1 ≤i,j ≤ v} =r,which is denoted by r-MOLS(v).It has been proved that there does not exist an r-MOLS(v) for r ∈ {v + 1,v2-1}.If M is the(3,2,1)-conjugate of L,then L is called to be(3,2,1)-conjugate r-orthogonal,as denoted by(3,2,1)-r-COLS(v).In this paper,the nonexistence of(3,2,1)-r-COLS(v) for r∈{v+2,v+3,v+5} is proved.更多还原