Details:
Title  Gröbner–Shirshov basis for the braid group in the Artin–Garside generators  Author(s)  Leonid A. Bokut  Type  Article in Journal  Abstract  Using [Bokut, L., Fong, Y., Ke, W.F., Shiao, LS., 2003. Gröbner–Shirshov basis for the braid semigroup. In: Shum, K.P. (Ed.), Advances in Algebra and Related Topics. Proceedings of the ICM2002 Satellite Conference on Algebra, Hong Kong. World Scientific, River Edge, pp. 14–25], we find a Gröbner–Shirshov basis S for the braid group B_n+1 in the Artin–Garside generators. We prove that S irreducible words of the B_n+1 coincide with the Garside normal form words. It gives a new proof of the uniqueness of the Garside normal form of a word, as well as a new proof that the semigroup B_n+1^+ of positive braids is a subsemigroup into B_n+1.  Keywords  Gröbner–Shirshov basis, Braid group, Garside normal form  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107001447 
Language  English  Journal  Journal of Symbolic Computation  Volume  43  Number  6–7  Pages  397  405  Year  2008  Note  Special issue on ASCM 2005  Edition  0  Translation 
No  Refereed 
No 
