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Latin squares with no proper subsquares

โœ Scribed by Katherine Heinrich


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
445 KB
Volume
29
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES


Orthogonal latin squares with subsquares
โœ L Zhu ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 275 KB

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 i

Latin squares with one subsquare
โœ I. M. Wanless ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 207 KB
Most Latin Squares Have Many Subsquares
โœ B.D McKay; I.M Wanless ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 227 KB

A k\_n Latin rectangle is a k\_n matrix of entries from [1, 2, ..., n] such that no symbol occurs twice in any row or column. An intercalate is a 2\_2 Latin subrectangle. Let N(R) be the number of intercalates in R, a randomly chosen k\_n Latin rectangle. We obtain a number of results about the dist

Existence of orthogonal latin squares wi
โœ Katherine Heinrich; L Zhu ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

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โœ B. Du ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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.