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Sets of mutually orthogonal Latin squares with “like subsquares”

✍ Scribed by Charles E Roberts Jr.

Book ID
107885178
Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
708 KB
Volume
61
Category
Article
ISSN
0097-3165

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📜 SIMILAR VOLUMES

Orthogonal latin squares with subsquares
Orthogonal latin squares with subsquares
✍ L Zhu 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 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

Maximal sets of mutually orthogonal Lati
Maximal sets of mutually orthogonal Latin squares
✍ David A. Drake; G.H.J. van Rees; W.D. Wallis 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 444 KB

Maximal sets of s mutually orthogonal Latin squares of order v are constructed for infinitely many new pairs (s,v).

Existence of orthogonal latin squares wi
Existence of orthogonal latin squares with aligned subsquares
✍ Katherine Heinrich; L Zhu 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 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