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In this chapter, we introduce the symmetric and alternating groups and use these ideas to solve a famous $1,000 question of Samuel Loyd. This gives us a taste of how group theory can be used to solve “real world” problems. We go on to consider more general groups of a similar flavour, namely the Coxeter groups.

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Coxeter groups and the 15-puzzle

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  • 发表日期：

    2025年

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  • Chris Bowman

摘要

In this chapter, we introduce the symmetric and alternating groups and use these ideas to solve a famous $1,000 question of Samuel Loyd. This gives us a taste of how group theory can be used to solve “real world” problems. We go on to consider more general groups of a similar flavour, namely the Coxeter groups.