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Article Dans Une Revue International Journal of Algebra and Computation Année : 2006

On word reversing in braid groups

Résumé

It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a word by at most a linear factor depending on the group presentation only. We give a counter-example to this conjecture, but, on the other hand, we establish length upper bounds for the case when only right reversing is involved. We also state a new conjecture which would, like the above one, imply that the space complexity of the handle reduction algorithm is linear.
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Dates et versions

hal-00002227 , version 1 (19-07-2004)

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Patrick Dehornoy, Bert Wiest. On word reversing in braid groups. International Journal of Algebra and Computation, 2006, 16 (5), pp.941-957. ⟨hal-00002227⟩
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