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Abstract: Let W be a Coxeter group with Coxeter generators S. The rank of the Coxetersystem W,S is the cardinality |S| of S. The Coxeter system W,S has finiterank if and only if W is finitely generated. If W,S has infinite rank, then|S| = |W|, since every element of W is represented by a finite product ofelements of S. Thus if W is not finitely generated, the rank of W,S isuniquely determined by W. If W is finitely generated, then W may have sets ofCoxeter generators S and S- of different ranks. In this paper, we determine theset of all possible ranks for an arbitrary finitely generated Coxeter group W.

Autor: Michael L. Mihalik, John G. Ratcliffe

Fuente: https://arxiv.org/

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