2004/07/20 by Patrick Dehornoy, Dehornoy, Patrick, Bert Wiest +1
Mathematics · #20F10 #FOS: Mathematics #Group Theory (math.GR) #MSC 20F36 #math.GR #msc:20F10 #msc:20F36
paper · pdf · doi:10.48550/arxiv.math/0407333
arxiv created 2004/07/20 · arxiv updated 2009/12/01
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.