VARIATIONS IN WRITHES OF VIRTUAL KNOTS UNDER A LOCAL MOVE

n-writhes denoted by J(n)(K) are virtual knot invariants for n not equal 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 not equal 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.