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Groebner-Shirshov basis for the braid semigroup

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 Added by Leonid Bokut
 Publication date 2008
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and research's language is English




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We found Groebner-Shirshov basis for the braid semigroup $B^+_{n+1}$. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.



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152 - L. A. Bokut 2008
In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$ is the subsemigroup in $B_{n+1}$.
156 - L. A. Bokut 2008
In this paper, we obtain Groebner-Shirshov (non-commutative Grobner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new ``Garside word $delta$. It gives a new algorithm for getting the Birman-Ko-Lee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
172 - Yuqun Chen , Jianjun Qiu 2008
In this paper, a Groebner-Shirshov basis for the Chinese monoid is obtained and an algorithm for the normal form of the Chinese monoid is given.
107 - Yuqun Chen , Chanyan Zhong 2008
In this paper, we generalize the Shirshovs Composition Lemma by replacing the monomial order for others. By using Groebner-Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained.
A new construction of a free inverse semigroup was obtained by Poliakova and Schein in 2005. Based on their result, we find a Groebner-Shirshov basis of a free inverse semigroup relative to the deg-lex order of words. In particular, we give the (unique and shortest) Groebner-Shirshov normal forms in the classes of equivalent words of a free inverse semigroup together with the Groebner-Shirshov algorithm to transform any word to its normal form.
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