Region Polynomial of a Knot Diagram
. Sombir
Department of Mathematics and Statistics, CCS Haryana Agricultural University, Hisar, India.
Vikash Siwach *
Department of Mathematics and Statistics, CCS Haryana Agricultural University, Hisar, India.
*Author to whom correspondence should be addressed.
Abstract
We introduce a new polynomial for knot diagrams. The coefficients of this polynomial are dependent on the
number of the arcs on the regions of the knot diagrams. A relation between the sum of the coefficients and
the number of crossing of the knot diagram is developed. Some other properties of the developed region
based polynomial are explained. The behaviour of the polynomial against Reidemeister moves is also examined.
Keywords: knot diagram, crossing number, Reidemeister moves, warping polynomial