arXiv Analytics

Sign in

arXiv:0808.0573 [math.GT]AbstractReferencesReviewsResources

The dealternating number and the alternation number of a closed 3-braid

Tetsuya Abe, Kengo Kishimoto

Published 2008-08-05, updated 2008-12-10Version 2

We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.

Comments: We corrected Section 6
Categories: math.GT
Subjects: 57M25
Related articles: Most relevant | Search more
arXiv:1007.3278 [math.GT] (Published 2010-07-19, updated 2011-01-20)
Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
arXiv:1111.7000 [math.GT] (Published 2011-11-29, updated 2011-12-01)
A bound for orderings of Reidemeister moves
arXiv:1512.03592 [math.GT] (Published 2015-12-11)
An upper bound on stick numbers of knots

Links

Toolbox