In this chapter algebraic statistics methods are used for design of experiments generation. In particular the class of Gerechte designs, that includes the game of Sudoku, has been studied. The first part provides a review of the algebraic theory of indicator functions of fractional factorial designs. Then, a system of polynomial equations whose solutions are the coefficients of the indicator functions of all the Sudoku fractions is given for the general p^2 × p^2 case (p integer). The subclass of symmetric Sudoku is also studied. The 4 × 4 case has been solved using CoCoA. In the second part the concept of move between Sudoku has been investigated. The polynomial form of some types of moves between sudoku grids has been constructed. Finally, the key points of a future research on the link between Sudoku, contingency tables and Markov basis are summarised.
Indicator function and sudoku designs
ROGANTIN, MARIA PIERA
2009-01-01
Abstract
In this chapter algebraic statistics methods are used for design of experiments generation. In particular the class of Gerechte designs, that includes the game of Sudoku, has been studied. The first part provides a review of the algebraic theory of indicator functions of fractional factorial designs. Then, a system of polynomial equations whose solutions are the coefficients of the indicator functions of all the Sudoku fractions is given for the general p^2 × p^2 case (p integer). The subclass of symmetric Sudoku is also studied. The 4 × 4 case has been solved using CoCoA. In the second part the concept of move between Sudoku has been investigated. The polynomial form of some types of moves between sudoku grids has been constructed. Finally, the key points of a future research on the link between Sudoku, contingency tables and Markov basis are summarised.
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