| Project/Area Number |
23540057
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
NAKANO Tetsuo 東京電機大学, 理工学部, 教授 (00217796)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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| Keywords | Booleanグレブナ基底 / 井上アルゴリズム / 数独型パズル / Boolean グレブナ基底 / 井上不変量 / 点付き代数曲線 / モジュライ空間 / 単項曲線の変形空間 / Boolean Groebner Bases / 代数的組合せ論 / グレブナ基底 / Bool 環 / toric 多様体 |
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| Outline of Final Research Achievements |
In this research, we have studied the Inoue algorithm, which is a very efficient method for solving a system of the Boolean polynomial equations, and its application to the puzzles of Sudoku type. We have firstly defined the Inoue invariant of such a system, which is the triple data of the minimum tree diagram among all the trees appearing in the process of the generalized Inoue algorithm. As an application, using the formulation of the puzzles of Sudoku type in terms of the Boolean polynomial equations, we have classified the Inoue invariant of the 4-doku and the diagonal 5-doku puzzles. It turns out that in these cases, every puzzle with a unique solution has a trivial Inoue invariant (2,1,1) except 2 special types of diagonal 5-doku puzzles. We have also shown by experiments that, in the case of Sudoku puzzles (9 times 9), the Inoue invariant is an excelent indicator of the difficulty of the puzzles.
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