We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate and having its (3, 2, 1)-conjugate also a diagonal Latin square as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it c
Doubly diagonal orthogonal latin squares
β Scribed by Katherine Heinrich; A.J.W. Hilton
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 448 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this article we give some new constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n β‘ 0, 1 (mod 4),
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.
## Abstract We shall refer to a diagonal Latin square which is orthogonal to its (3,1,2)βconjugate, and the latter is also a diagonal Latin square, as a (3,1, 2)βconjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it contai