| CONSTRUCTING SELF-CONJUGATE SELF-ORTHOGONAL DIAGONAL LATIN SQUARES |
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| 引用本文： | 杜北. CONSTRUCTING SELF-CONJUGATE SELF-ORTHOGONAL DIAGONAL LATIN SQUARES[J]. 应用数学学报(英文版), 1998, 14(3): 324-327. DOI: 10.1007/BF02677413 |
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| 作者姓名： | 杜北 |
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| 作者单位： | Deportment of Mathematics，Suzhou University，Such on 215006，China |
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| 摘 要： | 1.IntroductionALatinsquareofordernisannxnarraysuchthateveryrowandeverycolumnisapermutationofann-setN.AtransversalinaLatinsquareisasetofpositions,oneperrowandonepercolumn,amongwhichthesymbolsoccurpreciselyonceeach.AdiagonalLatinsquareisaLatinsquarewhosemaindiagonalandbackdiagonalarebothtransversals.TwoLatinsquaresofordernareorthogonalifeachsymbolinthefirstsquaremeetseachsymbolinthesecondsquareexactlyoncewhentheyaresuperposed.ALatinsquareisself-orthogonalifitisorthogonaltoitstranspose.Inanea…
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| 收稿时间： | 1995-05-31 |
Constructing self-conjugate self-orthogonal diagonal latin squares |
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| Du Beiliang. Constructing self-conjugate self-orthogonal diagonal latin squares[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(3): 324-327. DOI: 10.1007/BF02677413 |
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| Authors: | Du Beiliang |
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| Affiliation: | (1) Department of Mathematics, Suzhou University, 215006 Suzhou, China |
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| Abstract: | In this paper, we give some constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions we disproof the conjecture about SCSODLS and show that there exist SCSODLS of orderV, whenevervэ1 (mod 12), with the possible exception ofvε{13, 85, 133}. |
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| Keywords: | Diagonal Latin square Schroder quasigroup group divisible design |
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