Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they a...Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they are all idempotent. In this paper, we show that for any integer v≥28, there exists an r-MOILS（v） if and only if r∈[v, v^2]／ {v ＋ 1, v^2-1}.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.61373007,11371208Zhejiang Provincial Natural Science Foundation of China under Grant No.LY13F020039Sponsored by K.C.Wong Magna Fund in Ningbo University
文摘Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they are all idempotent. In this paper, we show that for any integer v≥28, there exists an r-MOILS（v） if and only if r∈[v, v^2]／ {v ＋ 1, v^2-1}.
