The winning strategy for Hironaka's polyhedra game is almost arbitrary

Sheng Ming Ma; Zhiming Zheng

doi:10.1016/j.jpaa.2010.12.005

The winning strategy for Hironaka's polyhedra game is almost arbitrary

Sheng Ming Ma^*
, Zhiming Zheng

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	2154-2164
页数	11
期刊	Journal of Pure and Applied Algebra
卷	215
期	9
DOI	https://doi.org/10.1016/j.jpaa.2010.12.005
出版状态	已出版 - 9月 2011

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10.1016/j.jpaa.2010.12.005

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title = "The winning strategy for Hironaka's polyhedra game is almost arbitrary",

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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AB - 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.

UR - https://www.scopus.com/pages/publications/79953723450

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DO - 10.1016/j.jpaa.2010.12.005

M3 - 文章

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The winning strategy for Hironaka's polyhedra game is almost arbitrary

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