Belolipetsky MV and Gunnells PE
Groups defined by presentations of the form â�¨s1,...,sn | si2 = 1, (sisj)mij = 1(i,j=1,...,n)â�© are called Coxeter groups. The exponents mi,j ∈ N ∪ { ∞ } form the Coxeter matrix, which characterizes the group up to isomorphism. The Coxeter groups that are most important for applications are the Weyl groups and affine Weyl groups. For example, the symmetric group Sn is isomorphic to the Coxeter group with presentation â�¨s1,...,sn | si2 = 1 (i=1,...,n),(sisi+1)3=1(i=1,...,n-1)â�©, and is also known as the Weyl group of type An-1.
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