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ARC SHIFT NUMBER AND REGION ARC SHIFT NUMBER FOR VIRTUAL KNOTS
Gill, Amrendra,Kaur, Kirandeep,Madeti, Prabhakar Korean Mathematical Society 2019 대한수학회지 Vol.56 No.4
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtual knot diagram can be turned into trivial knot using arc shift (region arc shift) moves. Based upon the arc shift move and region arc shift move, we define two virtual knot invariants, arc shift number and region arc shift number respectively.
VARIATIONS IN WRITHES OF VIRTUAL KNOTS UNDER A LOCAL MOVE
Amrendra Gill,Prabhakar Madeti 대한수학회 2022 대한수학회보 Vol.59 No.2
n-writhes denoted by Jn(K) are virtual knot invariants for n 6= 0 and are closely associated with coecients of some polynomial invariants of virtual knots. In this work, we investigate the variations of Jn(K) under arc shift move and conclude that n-writhes Jn(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n 6= 0 we provide an innite family of virtual knots which can be distinguished by n-writhes Jn(K), whereas odd writhe J(K) fails to do so.
On Minimal Unknotting Crossing Data for Closed Toric Braids
Siwach, Vikash,Prabhakar, Madeti Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.2
Unknotting numbers for torus knots and links are well known. In this paper, we present a new approach to determine the position of unknotting number crossing changes in a toric braid such that the closure of the resultant braid is equivalent to the trivial knot or link. Further we give unknotting numbers of more than 600 knots.
Arc shift number and Region arc shift number for virtual knots
Amrendra Gill,Kirandeep Kaur,Prabhakar Madeti 대한수학회 2019 대한수학회지 Vol.56 No.4
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtual knot diagram can be turned into trivial knot using arc shift (region arc shift) moves. Based upon the arc shift move and region arc shift move, we define two virtual knot invariants, arc shift number and region arc shift number respectively.