| Title:
|
On orthogonal Latin $p$-dimensional cubes (English) |
| Author:
|
Trenkler, Marián |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
725-728 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a construction of $p$ orthogonal Latin $p$-dimensional cubes (or Latin hypercubes) of order $n$ for every natural number $n\ne 2,6$ and $p \ge 2$. Our result generalizes the well known result about orthogonal Latin squares published in 1960 by R. C. Bose, S. S. Shikhande and E. T. Parker. (English) |
| Keyword:
|
Latin $p$-dimensional cube |
| Keyword:
|
Latin hypercube |
| Keyword:
|
Latin squares |
| Keyword:
|
orthogonal |
| MSC:
|
05B15 |
| idZBL:
|
Zbl 1081.05016 |
| idMR:
|
MR2153097 |
| . |
| Date available:
|
2009-09-24T11:27:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128017 |
| . |
| Reference:
|
[1] R. C. Bose, S. S. Shrikhande and E. T. Parker: Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture.Canad. J. Math. 12 (1960), 189–203. MR 0122729, 10.4153/CJM-1960-016-5 |
| Reference:
|
[2] J. Dénes and A. D. Keedwel: Latin Squares and Their Applications.Akadémiai Kiadó, Budapest, 1974. MR 0351850 |
| Reference:
|
[3] G. L. Mullen: Orthogonal hypercubes and related designs.J. Stat. Plann. Inference 73 (1998), 177–188. Zbl 0935.62089, MR 1655219, 10.1016/S0378-3758(98)00059-7 |
| Reference:
|
[4] M. Trenkler: Magic $p$-dimensional cubes of order $n \lnot \equiv 2\hspace{4.44443pt}(\@mod \; 4)$.Acta Arithmetica 92 (2000), 189–194. MR 1750318 |
| . |
