6 papers · 1 filter
A refinement of the Q-Polynomial for twisted knots
Tumpa Mahato, Prabhakar Madeti
This paper introduces a two-variable polynomial invariant for oriented twisted knots, denoted by , refining the -polynomial of N. Kamada and S. Kamada \cite{NaoS…
Arc shift move and region arc shift move for twisted knots
Tumpa Mahato, Prabhakar Madeti
In this paper, we study the unknotting operation for twisted knots, called arc shift move. First, we find a family of twisted knots with arc shift number for any given $n \in \…
Parametrizing some interesting knotted surfaces
Louis H. Kauffman, Tumpa Mahato, Rama Mishra
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
Isolated regions of a link projection
Tumpa Mahato, Ayaka Shimizu
A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum val…
Non-triviality of welded knots and ribbon torus-knots
Tumpa Mahato, Rama Mishra, Sahil Joshi
In this paper we study welded knots and their invariants. We focus on generating examples of non-trivial knotted ribbon tori as the tube of welded knots that are obtained from clas…
Polynomially knotted 2-spheres
Rama Mishra, Tumpa Mahato
We review the polynomial parameterization of classical knots and prove the analogous results for long knots. We also construct polynomial parameterizations for certain classes…