The winning strategy for Hironaka’s polyhedra game is almost arbitrary |
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| Authors: | Sheng-Ming Ma Zhiming Zheng |
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| Institution: | a LMIB and Ecole Centrale de Pékin, Beihang University, No.37 Xueyuan Road, Haidian District, Beijing 100191, Chinab Key Laboratory of Mathematics, Informatics and Behavioral Semantics of the Ministry of Education, Beihang University, No.37 Xueyuan Road, Haidian District, Beijing 100191, China |
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| Abstract: | This paper proves that the winning strategy for Hauser’s version of Hironaka’s polyhedra game is almost arbitrary. The winning strategy and its associated invariants are based on an algorithm of matrix triangulations and matrix diagonalizations. It is proved that if a set sequence constitutes a winning strategy for the game, then so does every set sequence containing it. The same holds for Hironaka’s version of the game if every move is permissible. |
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| Keywords: | 14B05 52B20 |
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