%0 Journal Article %T Gr£¿bner-Shirshov bases for braid groups in Adyan-Thurston generators %A Yuqun Chen %A Chanyan Zhong %J Mathematics %D 2009 %I arXiv %X In this paper, we give a Gr\"obner-Shirshov basis of the braid group $B_{n+1}$ in Adyan-Thurston generators. We also deal with the braid group of type $\bf{B}_{n}$. As results, we obtain a new algorithm for getting the Adyan-Thurston normal form, and a new proof that the braid semigroup $B^+_{n+1}$ is the subsemigroup in $B_{n+1}$. %U http://arxiv.org/abs/0909.3639v1