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Orthogonal latin squares with subsquares

✍ Scribed by L Zhu

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
275 KB
Volume
48
Category
Article
ISSN
0012-365X

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✦ Synopsis

Denote by LS(v, n) a pair of orthogonal latin squares of side v with orthogonal subsquares of side n. It is proved by using a generalized singular direct product that for every odd integer n ~>304 or every even integer n ~> 304 in some infinite families, an LS(v, n) exists if and only if v>~3n. It is also proved that for every integer n~>304, an LS(v, n) exists if v>3n+6.

πŸ“œ SIMILAR VOLUMES

Existence of orthogonal latin squares wi
Existence of orthogonal latin squares with aligned subsquares
✍ Katherine Heinrich; L Zhu πŸ“‚ Article πŸ“… 1986 πŸ› Elsevier Science 🌐 English βš– 600 KB

It is shown that for both v and n even, v > n > 0, there exists a pair of orthogonal latin squares of order v with an aligned subsquare of order n if and only if v ~> 3n, v ~ 6, n 4= 2, 6. This is the final case in showing that the above result is true for all v J: 6 and for all n ~ 2, 6. When n = 6

The existence of orthogonal diagonal Lat
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✍ B. Du πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 518 KB

We prove that there exists a pair of orthogonal diagonal Latin squares of order v with missing subsquares of side n (ODLS(v,n)) for all v ~> 3n + 2 and v -n even. Further, there exists a magic square of order v with missing subsquare of side n (MS(v, n)) for all v ~> 3n + 2 and v -n even.

Latin squares with one subsquare
Latin squares with one subsquare
✍ I. M. Wanless πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 207 KB