宁波大学学报(理工版)
寧波大學學報(理工版)
저파대학학보(리공판)
JOURNAL OF NINGBO UNIVERSITY(NSEE)
2010年
1期
118-122
,共5页
拉丁方%r-正交%(3%2%1)-共轭
拉丁方%r-正交%(3%2%1)-共軛
랍정방%r-정교%(3%2%1)-공액
latin square%r-orthogonal%(3,2,1)-conjugate
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.
2箇v階拉丁方,L=(lij)和M=(mij)被稱為是r-正交的,如果把它們重疊起來可以得到恰好r箇不同的有序元素偶,即|{(lij,mij):1≤i,j≤v}|=r,記為r-MOLS(v).r-MOLS(v)在r∈{v+1,v2-1}上的不存在性已經得到證明.如果M是L的(3,2,1)-共軛,可認為L是(3,2,1)-共軛r-正交的,可記為(3,2,1)-r-COLS(v).併且證明瞭(3,2,1)-r-COLS(v)在r∈{v+2,v+3,v+5}上的不存在性.
2개v계랍정방,L=(lij)화M=(mij)피칭위시r-정교적,여과파타문중첩기래가이득도흡호r개불동적유서원소우,즉|{(lij,mij):1≤i,j≤v}|=r,기위r-MOLS(v).r-MOLS(v)재r∈{v+1,v2-1}상적불존재성이경득도증명.여과M시L적(3,2,1)-공액,가인위L시(3,2,1)-공액r-정교적,가기위(3,2,1)-r-COLS(v).병차증명료(3,2,1)-r-COLS(v)재r∈{v+2,v+3,v+5}상적불존재성.
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 e {v +1, v2 -1}. If M is the (3,2,1 )-conjugate of L, then L is called to be (3,2,l)-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 re {v+2,v+3,v+5} is proved.