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Matsumoto's theorem (group theory)
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Matsumoto's theorem (group theory) : ウィキペディア英語版
Matsumoto's theorem (group theory)
In group theory, Matsumoto's theorem, proved by , gives conditions for two reduced words of a Coxeter group to represent the same element.
==Statement==

If two reduced words represent the same element of a Coxeter group, then Matsumoto's theorem states that the first word can be transformed into the second by repeatedly transforming
:''xyxy...'' to ''yxyx...'' (or vice versa)
where
:''xyxy... = yxyx...''
is one of the defining relations of the Coxeter group.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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