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 q x q case, where q is the square of an integer. The subclass of symmetric sudoku is also studied. The 4x4 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 / Fontana, Roberto; Rogantin, M. P. - In: Algebraic and Geometric Methods in Statistics / GIBILISCO P.; RICCOMAGNO E.; PISTONE G.; WYNN H. P.. - [s.l] : Cambridge University Press, 2009. - ISBN 9780521896191. - pp. 203-224

### Indicator function and sudoku designs

#### 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 q x q case, where q is the square of an integer. The subclass of symmetric sudoku is also studied. The 4x4 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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2009
9780521896191
Algebraic and Geometric Methods in Statistics
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2264007`
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