On the Spectrum of Mutually r-orthogonal Idempotent Latin Squares

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...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 31; no. 3; pp. 813 - 822
Main Author Xu, Yun-qing
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2015
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
幂等
拉丁方
整数
正交
正方形
idempotent
orthogonal
Latin square
05B15
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Summary: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}.
Bibliography: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}.
11-2041/O1
Latin square r-orthogonal idempotent
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-015-0507-z