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Permutation matrices related to Sudoku. (English) Zbl 1173.05306
Summary: We consider a class of permutation matrices associated with the popular game of Sudoku, and prove some connectivity and existence results for this matrix class.
MSC:
05B20Matrices (incidence, Hadamard, etc.)
15A36Matrices of integers (MSC2000)
References:
[1]Bóna, M.: Combinatorics of permutations, (2004)
[2]Brualdi, R. A.: Combinatorial matrix classes, (2006)
[3]Brualdi, R. A.; Ryser, H. J.: Combinatorial matrix theory, (1991) · Zbl 0746.05002
[4]D. Eppstein, Nonrepetitive paths and cycles in graphs with application to Sudoku, 2005, arXive:cs/0507053.
[5]Hayes, B.: Unwed numbers – the mathematics of sudoku a puzzle that boastsno math required, Amer. sci. 94, 12-15 (2006)
[6]A.C. Bartlett, A.N. Langville, An integer programming model for the Sudoku problem, Preprint, Department of Mathematics, College of Charleston, South Carolina, 2006.
[7]T. Yato, Complexity and completeness of finding another solution and its application to puzzles, Master thesis, Graduate School of Science, University of Tokyo, 2003.