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A001438 Maximal number of mutually orthogonal Latin squares (or MOLS) of order n. 1
1, 2, 3, 4, 1, 6, 7, 8 (list; graph; refs; listen; history; text; internal format)



CRC Handbook of Combinatorial Designs, 1996, pp. 113ff.

S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays, Springer-Verlag, NY, 1999, Chapter 8.

David Joyner and Jon-Lark Kim, Kittens, Mathematical Blackjack, and Combinatorial Codes, Chapter 3 in SELECTED UNSOLVED PROBLEMS IN CODING THEORY, Applied and Numerical Harmonic Analysis, Springer, 2011, pp. 47-70, DOI: 10.1007/978-0-8176-8256-9_3; http://www.springerlink.com/content/w6t033u9607k4834/.

E. T. Parker, Attempts for orthogonal latin 10-squares, Abstracts Amer. Math. Soc., Vol. 12 1991 #91T-05-27.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, pp. 58 Penguin Books 1997.


Table of n, a(n) for n=2..9.

Anonymous, Order-10 Greco-Latin square

R. C. Bose & S. S. Shrikhande, On The Falsity Of Euler's Conjecture About The Non-Existence Of Two Orthogonal Latin Squares Of Order 4t+2

C. J. Colbourn & J. H. Dinitz, Mutually Orthogonal Latin Squares:A Brief Survey of Constructions

M. Dettinger, Euler's Square

E. T. Parker, Orthogonal Latin Squares

E. Parker-Woodruff, Greco-Latin Squares Problem

Eric Weisstein's World of Mathematics, Euler's Graeco-Roman Squares Conjecture

Index entries for sequences related to Latin squares and rectangles


Sequence in context: A129708 A071518 A065338 * A105587 A049073 A076388

Adjacent sequences:  A001435 A001436 A001437 * A001439 A001440 A001441




N. J. A. Sloane.


By convention, a(0) = a(1) = infinity. Parker and others conjecture that a(10) = 2. It is also known that a(11) = 10, a(12) >= 5.



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Last modified December 20 12:05 EST 2014. Contains 252241 sequences.