论文信息 - Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle

Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle

Given any knot diagram E, we present a sequence of knot diagrams of the same knot type for which the minimum number of Reidemeister moves required to pass to E is quadratic with respect to the number of crossings. These bounds apply both in S2 and in ℝ2.

Joel Hass | Tahl Nowik | J. Hass | Tahl Nowik

[1] J. W. Alexander,et al. On Types of Knotted Curves , 1926 .

[2] J. Lagarias,et al. The number of Reidemeister moves needed for unknotting , 1998, math/9807012.

[3] Tobias J. Hagge. Every Reidemeister move is needed for each knot type , 2004, math/0404145.

[4] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[5] S. Pollard. On Plane Curves , 1928 .

[6] Mohamed Elhamdadi,et al. A lower bound for the number of Reidemeister moves of type III , 2005, math/0501490.

[7] Jack Snoeyink,et al. The Size of Spanning Disks for Polygonal Curves , 2003, Discret. Comput. Geom..

[8] G. Budworth. The Knot Book , 1983 .

[9] Joel Hass,et al. Invariants of knot diagrams , 2007, 0708.2509.

[10] Olof-Petter OEstlund. Invariants of knot diagrams and relations among Reidemeister moves , 2000 .

[11] V. Arnold. Plane curves, their invariants, Perestroikas, and classifications , 1994 .

[12] C. Adams. Tales of Topology. (Book Reviews: The Knot Book. An Elementary Introduction to the Mathematical Theory of Knots.) , 1994 .

[13] C. Hayashi,et al. A LOWER BOUND FOR THE NUMBER OF REIDEMEISTER MOVES FOR UNKNOTTING , 2006 .

[14] K. Reidemeister,et al. Knoten und Gruppen , 1927 .