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Algorithmic solutions to the conjugacy problem in the braid groups B n ,n =2, 3, 4, ... were given in earlier work. This note concerns the computation of two integer class invariants, known as ''inf'' and ''sup.'' A key issue in both algorithms is the number m of times one must ''cycle'' (resp. ''decycle'') in order to either increase inf (resp. decrease sup) or to be sure that it is already...
A new presentation of then-string braid groupB n is studied. Using it, a new solution to the word problem inB n is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes possible certain computational improvements. We also give a related solution to the conjugacy problem, but the improvements in its complexity are not clear...
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