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On the spectrum of r-self-orthogonal Latin squares

✍ Scribed by Yunqing Xu; Yanxun Chang

Book ID
104113346
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
295 KB
Volume
279
Category
Article
ISSN
0012-365X

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✦ Synopsis

Two Latin squares of order n are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the transpose of the ÿrst one, we say that the ÿrst square is r-self-orthogonal, denoted by r-SOLS(n). It has been proved that the necessary condition for the existence of an r-SOLS(n) is n 6 r 6 n 2 and r ∈ {n + 1; n 2 -1}. Zhu and Zhang conjectured that there is an integer n0 such that for any n ¿ n0, there exists an r-SOLS(n) for any r ∈ [n; n 2 ] -{n + 1; n 2 -1}. In this paper, we show that n0 6 28.

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✍ F. E. Bennett; B. Du; H. Zhang πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 229 KB πŸ‘ 1 views

In this article we give some new constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n ≑ 0, 1 (mod 4),