The fine structures of three Latin squares
β Scribed by Yanxun Chang; Giovanni Lo Faro; Giorgio Nordo
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 255 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Denote by Fin(Ο ) the set of all integral pairs (t,s) for which there exist three Latin squares of order Ο on the same set having fine structure (t,s). We determine the set Fin(Ο ) for any integer vββ₯β9. Β© 2005 Wiley Periodicals, Inc. J Combin Designs 14: 85β110, 2006
π SIMILAR VOLUMES
## Abstract A latin square __S__ is isotopic to another latin square __S__β² if __S__β² can be obtained from __S__ by permuting the row indices, the column indices and the symbols in __S__. Because the three permutations used above may all be different, a latin square which is isotopic to a symmetric
## Abstract An autotopism of a Latin square is a triple (Ξ±, Ξ², Ξ³) of permutations such that the Latin square is mapped to itself by permuting its rows by Ξ±, columns by Ξ², and symbols by Ξ³. Let Atp(__n__) be the set of all autotopisms of Latin squares of order __n__. Whether a triple (Ξ±, Ξ², Ξ³) of pe
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.