Region Polynomial of a Knot Diagram

Abstract

We introduce a new polynomial for knot diagrams. The coefficients of this polynomial are dependent on thenumber of the arcs on the regions of the knot diagrams. A relation between the sum of the coefficients andthe number of crossing of the knot diagram is developed. Some other properties of the developed regionbased polynomial are explained. The behaviour of the polynomial against Reidemeister moves is also examined.