Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-16T16:46:02.566Z Has data issue: false hasContentIssue false
  • English
  • Français

MUTUALLY ORTHOGONAL FAMILIES OF LINEAR SUDOKU SOLUTIONS

Part of: Designs and configurations

Published online by Cambridge University Press:  15 December 2009

JOHN LORCH
JOHN LORCH*
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, IN 47306-0490, USA (email: jlorch@bsu.edu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 must lie in the same orbit of a symmetry group preserving sudoku solutions.

Keywords

sudokusudoku grouporthogonal latin squaresmutually orthogonal latin squares

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 409 - 420
Copyright
Copyright © Australian Mathematical Publishing Association, Inc. 2009

References

[1]Bailey, R., Cameron, P. and Connelly, R., ‘Sudoku, Gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes’, Amer. Math. Monthly 115(5) (2008), 383–404.CrossRefGoogle Scholar
[2]Bose, R. and Shrikhande, S., ‘On the construction of sets of mutually orthogonal latin squares and the falsity of a conjecture of Euler’, Trans. Amer. Math. Soc. 95 (1960), 191–209.CrossRefGoogle Scholar
[3]Bose, R., Shrikhande, S. and Parker, E., ‘Further results on the construction of mutually orthogonal latin squares and the falsity of Euler’s conjecture’, Canad. J. Math. 12 (1960), 189–203.CrossRefGoogle Scholar
[4]Burton, D., Elementary Number Theory (Allyn and Bacon, Boston, 1980).Google Scholar
[5]Colbourn, C. and Dinitz, J., ‘Mutually orthogonal latin squares: a brief survey of constructions’, J. Statist. Plann. Inference 95 (2001), 9–48.CrossRefGoogle Scholar
[6]Euler, L., Recherches sur une nouvelle espèce de quarrés magiques, Opera Omnia Series I, vol. VII (Teubner, Leipzig, Berlin, 1923), pp. 291–392.Google Scholar
[7]Felgenhauer, B. and Jarvis, F., ‘Mathematics of sudoku I’, Math. Spectrum 39 (2006), 15–22.Google Scholar
[8]Fincher, C. and Mantini, L., ‘Orthogonal sudoku puzzles and combing transversals’. Preprint.Google Scholar
[9]Golomb, S., ‘Problem 11214’, Amer. Math. Monthly 113(3) (2006), 268. Problem section (eds. G. Edgar, D. Hensley and D. West).CrossRefGoogle Scholar
[10]Herzberg, A. and Ram Murty, M., ‘Sudoku squares and chromatic polynomials’, Notices Amer. Math. Soc. 54(6) (2007), 708–717.Google Scholar
[11]Jarvis, F. and Russell, E., ‘Mathematics of sudoku II’, Math. Spectrum 39 (2006), 54–58.Google Scholar
[12]Keedwell, A., ‘On sudoku squares’, Bull. Inst. Combin. Appl. 50 (2007), 52–60.Google Scholar
[13]Lorch, C. and Lorch, J., ‘Enumerating small sudoku puzzles in a first abstract algebra course’, PRIMUS 18 (2008), 149–158.CrossRefGoogle Scholar
[14]MacNeish, H., ‘Euler squares’, Ann. Math. 23 (1922), 221–227.CrossRefGoogle Scholar
[15]Mullen, G., ‘A candidate for the “next Fermat problem”’, Math. Intelligencer 17 (1995), 18–22.CrossRefGoogle Scholar
[16]Pedersen, R. and Vis, T., ‘Sets of mutually orthogonal sudoku latin squares’, College Math J. 40 (2009), 174–180.CrossRefGoogle Scholar
[17]Roberts, F., Applied Combinatorics (Prentice Hall, Engelwood Cliffs, NJ, 1984).Google Scholar