Let N(n) denote the maximum numner of mutually orthogonal Latin squares of order n. II is shown that N(n) 3 7 for n > 4922.
On orthogonal latin squares
โ Scribed by C.F Woodcock
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 115 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract An orthogonal latin square graph (OLSG) is one in which the vertices are latin squares of the same order and on the same symbols, and two vertices are adjacent if and only if the latin squares are orthogonal. If __G__ is an arbitrary finite graph, we say that __G__ is realizable as an O
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