Abstract
In 2008, Bokut obtained a Gröbner–Shirshov basis [Formula: see text] of the braid group [Formula: see text] in the Artin–Garside generators and showed that [Formula: see text]-irreducible words of the [Formula: see text] coincided with the Garside normal forms of words. Using this basis [Formula: see text], we obtain the concrete expression of the [Formula: see text]-irreducible words, i.e. normal forms, of the [Formula: see text], and hence give a new understanding of the word problem and Garside normal forms of braid groups.
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