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 no proper subsquares
โ Scribed by Katherine Heinrich
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 445 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
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
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.