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Journal of Combinatorial Designs, ISSN 1063-8539, 09/2019, Volume 27, Issue 9, pp. 541 - 551
Commonly, the direct construction and the description of mutually orthogonal Latin squares (MOLS) make use of difference or quasi‐difference matrices. Now... 
bounds | permutation code | mutually orthogonal Latin squares | isometry | permutation arrays | MATHEMATICS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2014, Volume 47, Issue 43, pp. 435303 - 23
We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime... 
Latin squares | finite fields | phase space | mutually unbiased bases | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | UNBIASED BASES | Isomorphism | Permutations | Equivalence | Arrays | Mathematical analysis | Joints | Physics - Quantum Physics
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 11/2019, Volume 795, pp. 312 - 325
We introduce the orthogonal colouring game, in which two players alternately colour vertices (from a choice of m∈N colours) of a pair of isomorphic graphs... 
Orthogonal colouring game | Orthogonal graph colouring | Scoring game | Mutually orthogonal Latin squares | Games on graphs | Strictly matched involution | CHROMATIC NUMBER | COMPUTER SCIENCE, THEORY & METHODS | Computer Science | Discrete Mathematics
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2016, Volume 32, Issue 4, pp. 1353 - 1374
A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for... 
Mutually nearly orthogonal Latin squares | Difference covering array | Latin squares | Mathematics | Pseudo-orthogonal Latin squares | Engineering Design | Combinatorics | 05B15 | MATHEMATICS | MATRICES | COMBINATORIAL DESIGN | Graphs | Construction | Arrays | Symbols | Combinatorial analysis | Mathematics - Combinatorics
Journal Article
by Zhang, Y and Chen, J and Wu, D and Zhang, H
Utilitas Mathematica, ISSN 0315-3681, 09/2017, Volume 104, pp. 83 - 102
Let N = {0,1, ... , n-1}. A pair of orthogonal Latin squares A, B of order n is called diagonally ordered (DOOLS(n) for short) if the following properties are... 
Elementary | Frame mutually orthogonal Latin squares | Strong symmetric | Diagonally ordered magic square | EXISTENCE | MATHEMATICS, APPLIED | frame mutually orthogonal Latin squares | elementary | strong symmetric | STATISTICS & PROBABILITY | ARRAYS
Journal Article
Journal of Combinatorial Theory. Series A, ISSN 0097-3165, 10/2017, Volume 151, pp. 146 - 201
Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the... 
Mutually orthogonal Latin squares | Edge-decompositions | MATHEMATICS | DENSE GRAPHS | PACKINGS | MINIMUM DEGREE | INTEGER
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 01/2020
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2011, Volume 311, Issue 12, pp. 1015 - 1033
Let a b = n 2 . We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either ⌈ b n ⌉ or ⌊ b n ⌋ times in... 
Orthogonal array | Latin rectangle | Mutually orthogonal Latin square | MATHEMATICS | Mathematical analysis | Rectangles | Symbols | Images
Journal Article
Communications in Statistics - Theory and Methods, ISSN 0361-0926, 08/2017, Volume 46, Issue 16, pp. 8155 - 8165
Journal Article
International Journal of Applied Engineering Research, ISSN 0973-4562, 09/2015, Volume 10, Issue 18, pp. 39425 - 39430
Journal Article
Cryptography and Communications, ISSN 1936-2447, 2010, Volume 2, Issue 2, pp. 221 - 231
There has been much interest in mutually unbiased bases (MUBs) and their connections with various other discrete structures, such as projective planes,... 
Finite fields | Mutually unbiased bases | Mutually orthogonal Latin squares | Quantum cryptography | Odd prime powers | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 23, pp. 6464 - 6469
The competition graph of a digraph D is the graph which has the same vertex set as D and has an edge between u and v if and only if there exists a vertex x in... 
Competition number | Complete multipartite graph | Mutually orthogonal Latin squares | Competition graph | Edge clique cover number | MATHEMATICS
Journal Article
Journal Article
European Journal of Operational Research, ISSN 0377-2217, 2006, Volume 173, Issue 2, pp. 519 - 530
This paper applies algorithms integrating Integer Programming (IP) and Constraint Programming (CP) to the Mutually Orthogonal Latin Squares (MOLS) problem. We... 
Integer programming | Mutually Orthogonal Latin Squares | Constraints satisfaction | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | integer programming | constraints satisfaction | mutually orthogonal Latin squares | SETS | Usage | Algorithms | Functions, Orthogonal | Tests, problems and exercises | Management science
Journal Article
Journal of Statistical Planning and Inference, ISSN 0378-3758, 03/2013, Volume 143, Issue 3, pp. 573 - 582
An (n×n)/ksemi-Latin square is an n×n square array in which nk distinct symbols (representing treatments) are placed in such a way that there are exactly k... 
Block design | Block design efficiency measures | Mutually orthogonal Latin squares | Semi-Latin square | DESIGN package for GAP | Construction and enumeration of combinatorial designs | Design optimality | Algebraic computation | STATISTICS & PROBABILITY | BLOCK-DESIGNS
Journal Article
Journal of Combinatorial Designs, ISSN 1063-8539, 06/2012, Volume 20, Issue 6, pp. 265 - 277
Let n and k be integers, with n>1 and k>0. An (n×n)/k semi‐Latin square S is an n×n array, whose entries are k‐subsets of an nk‐set, the set of symbols of S,... 
transitive permutation groups | Schur-optimality | mutually orthogonal Latin squares | semi-Latin squares | MATHEMATICS | NON-EXISTENCE | BLOCK-DESIGNS
Journal Article
Journal of Statistical Planning and Inference, ISSN 0378-3758, 2001, Volume 95, Issue 1, pp. 9 - 48
In the two centuries since Euler first asked about mutually orthogonal latin squares, substantial progress has been made. The biggest breakthroughs came in... 
Mutually orthogonal latin squares | Transversal design | Block design | Orthogonal array | 51E10 | 51E21 | 05B15 | 51E05 | 05B25 | 05B05 | EXISTENCE | orthogonal array | FINITE PROJECTIVE PLANES | transversal design | HUGHES PLANE | STATISTICS & PROBABILITY | block design | INCOMPLETE TRANSVERSAL DESIGNS | ORDER | mutually orthogonal latin squares | 4 MOLS | SUBSQUARES | SETS | SUBPLANES | SPECTRUM
Journal Article
Journal of the Australian Mathematical Society, ISSN 1446-7887, 12/2009, Volume 87, Issue 3, pp. 409 - 420
For a class of 'linear' sudoku solutions, we construct Mutually orthogonal families of maximal size for all square orders, and we show that all such solutions... 
Mutually orthogonal latin squares | Sudoku group | Orthogonal latin squares | Sudoku | MATHEMATICS | mutually orthogonal latin squares | sudoku | orthogonal latin squares | sudoku group
Journal Article
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