论文信息 - 2 8 Ja n 20 05 Minimal diagrams of classical knots

2 8 Ja n 20 05 Minimal diagrams of classical knots

We show that if a classical knot diagram satisfies a certain combinatorial condition then it is minimal with respect to the number of classical crossings. This statement is proved by using the Kauffman bracket and the construction of atoms and knots.

V. Manturov

[1] V. Manturov. Minimal diagrams of classical and virtual links , 2005, math/0501393.

[2] V. Manturov. The Khovanov complex for virtual links , 2005, math/0501317.

[3] Vassily Olegovich Manturov,et al. Long virtual knots and their invariants , 2004 .

[4] S. Wehrli. A Spanning Tree Model for Khovanov Homology , 2004, math/0409328.

[5] V. Manturov. KAUFFMAN-LIKE POLYNOMIAL AND CURVES IN 2-SURFACES , 2003 .

[6] L. Kauffman. Virtual Knot Theory , 1998, Eur. J. Comb..

[7] Louis H. Kauffman,et al. State Models and the Jones Polynomial , 1987 .