The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Sian-Kathryn Jones; Stephanie Perkins; Paul Roach

doi:10.1155/2012/760310

The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Sian-Kathryn Jones, Stephanie Perkins, Paul Roach

Faculty of Computing, Engineering and Science

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Abstract

A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given.

Original language	English
Pages (from-to)	1 - 6
Number of pages	6
Journal	International Journal of Combinatorics
Volume	2012
DOIs	https://doi.org/10.1155/2012/760310
Publication status	Published - 8 Nov 2012

Keywords

latin squares
sudoku
enumeration
symmetry group

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10.1155/2012/760310Licence: CC BY

Sudoku Roach 2012Final published version, 653 KBLicence: CC BY

Cite this

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AB - A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given.

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KW - enumeration

KW - symmetry group

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The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Abstract

Keywords

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