• Kyungpook Mathematical Journal
• /
• 제55권2호
• /
• pp.485-506
• /
• 2015

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

• 대한수학회보
• /
• 제59권2호
• /
• pp.303-318
• /
• 2022

n-writhes denoted by J_n(K) are virtual knot invariants for n ≠ 0 and are closely associated with coefficients of some polynomial invariants of virtual knots. In this work, we investigate the variations of J_n(K) under arc shift move and conclude that n-writhes J_n(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n ≠ 0 we provide an infinite family of virtual knots which can be distinguished by n-writhes J_n(K), whereas odd writhe J(K) fails to do so.