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Some New Maximal Sets of Mutually Orthogonal Latin Squares
Designs, Codes and Cryptography, 2003A set of \(t\) mutually orthogonal Latin squares is maximal if it cannot be embedded in a larger set. The problem of constructing such maximal sets can be formulated in a geometric language and is then part of Galois geometries. In the present paper a computer classification of maximal partial spreads of \(\text{PG}(3,4)\setminus \text{PG}(3,2)\) is ...
Patrick Govaerts +3 more
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Sets of Mutually Orthogonal Sudoku Latin Squares
The College Mathematics Journal, 2009Ryan Pedersen (Ryan.Pedersen@ucdenver.edu) received his B.S. in mathematics and his B.A. in physics from the University of the Pacific, and his M.S. in applied mathematics from the University of Colorado Denver, where he is currently finishing his Ph.D. His research is in the field of finite projective geometry.
Ryan M. Pedersen, Timothy L. Vis
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On the spectrum of mutually r-orthogonal idempotent Latin squares
Acta Mathematicae Applicatae Sinica, English Series, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Maximal Sets of Mutually Orthogonal Idempotent Latin Squares
Canadian Mathematical Bulletin, 1971It is a well-known trivial fact that for a given integer n there exists at most n — 2 pairwise orthogonal idempotent latin squares. In the following note we prove that for n a prime power there always exists n—2 such squares.
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On the number of mutually orthogonal partial latin squares
Ars Comb., 1996A partial latin square of order \(n\) is an \(n\times n\) array such that each of the integers \(1,2,\dots,n\) appears at most once in any row or column. Two partial latin squares are orthogonal if all ordered pairs of entries obtained by superimposing the two squares are distinct and a collection of partial latin squares is orthogonal if each pair of ...
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Mutually orthogonal Latin squares based on general linear groups
Designs, Codes and Cryptography, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Construction Techniques for Mutually Orthogonal Latin Squares
1995Recent developments concerning the construction of mutually orthogonal latin squares (MOLS) and incomplete MOLS are discussed. Some improvements in the number of MOLS are presented using Greig’s line-flip technique, and some new sets of incomplete MOLS found by computer search are presented. Finally, a variant of Wilson’s theorem is developed.
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Some results on complete permutation polynomials and mutually orthogonal Latin squares
Finite Fields Their Appl.C. K. Vishwakarma, Rajesh P. Singh
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Three mutually orthogonal idempotent Latin squares of order 18
Ars Comb., 1997By a construction that starts with the cyclic group of order \(17\), the authors get Latin squares as stated in the title.
Xiafu Zhang, Hangfu Zhang
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