Parity of sets of mutually orthogonal Latin squares [PDF]
Journal of Combinatorial Theory, Series A, 2017 Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits.
N. Francetic, S. Herke, Ian M. Wanless
semanticscholar +7 more sources
Mutually orthogonal latin squares based on cellular automata [PDF]
Designs, Codes, and Cryptography, 2019 We investigate sets of mutually orthogonal latin squares (MOLS) generated by cellular automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter d over an alphabet of q elements generates a Latin square ...
Luca Mariot +2 more
exaly +6 more sources
Concerning the number of mutually orthogonal latin squares
Discrete Mathematics, 1974 AbstractLet N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that for large n, N(n)≥n117−2In addition to a known number-theoretic result, the proof uses a new combinatorial construction which also allows a quick derivation of the existence of a pair of orthogonal squares of all orders n > 14.
Richard M. Wilson
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Mutually Orthogonal Sudoku Latin Squares and Their Graphs [PDF]
Graphs and Combinatorics, 2021 We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then use the eigenvalues to distinguish non-isomorphic Sudoku Latin squares.
Sho Kubota, Sho Suda, Akane Urano
semanticscholar +4 more sources
Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares
AKCE International Journal of Graphs and Combinatorics, 2021 The subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal
A. El-Mesady, Shaaban M. Shaaban
doaj +2 more sources
Enhanced Sampling of the Molecular Potential Energy Surface Using Mutually Orthogonal Latin Squares: Application to Peptide Structures [PDF]
Biophysical Journal, 2003 Namasivayam Gautham
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Enumerating extensions of mutually orthogonal Latin squares [PDF]
Designs, Codes and Cryptography, 2019 Two $$n \times n$$ n × n Latin squares $$L_1, L_2$$ L 1 , L 2 are said to be orthogonal if, for every ordered pair ( x , y ) of symbols, there are coordinates ( i , j ) such that $$L_1(i,j) = x$$ L 1 ( i , j ) = x and $$L_2(i,j) = y$$ L 2 ( i , j ) = y
Simona Boyadzhiyska +2 more
semanticscholar +6 more sources
On generalized strong complete mappings and mutually orthogonal Latin squares
Ars Mathematica Contemporanea, 2021 We present an application of generalized strong complete mappings to construction of a family of mutually orthogonal Latin squares. We also determine a cycle structure of such mapping which form a complete family of MOLS.
A. Muratovic-Ribic
semanticscholar +3 more sources
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates [PDF]
Discrete Mathematics, 2018 We show that any partial Latin square of order $n$ can be embedded in a Latin square of order at most $16n^2$ which has at least $2n$ mutually orthogonal mates.
D. Donovan, M. Grannell, Emine Yazıcı
semanticscholar +7 more sources
iMOLSDOCK: Induced-fit docking using mutually orthogonal Latin squares (MOLS) [PDF]
Journal of Molecular Graphics and Modelling, 2017 We have earlier reported the MOLSDOCK technique to perform rigid receptor/flexible ligand docking. The method uses the MOLS method, developed in our laboratory.
Sam Paul D, Namasivayam Gautham
exaly +2 more sources