Region Polynomial of a Knot Diagram

. Sombir; Vikash Siwach

doi:10.9734/cjast/2022/v41i403987

Research Article Open access CC BY 4.0

Region Polynomial of a Knot Diagram

. Sombir, Vikash Siwach

Current Journal of Applied Science and Technology · pp. 17–25 · Published 14 Nov 2022

10.9734/cjast/2022/v41i403987

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.

knot diagram crossing number Reidemeister moves warping polynomial

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. Sombir, Vikash Siwach (2022). Region Polynomial of a Knot Diagram. Current Journal of Applied Science and Technology , 17–25. https://doi.org/10.9734/cjast/2022/v41i403987

Affiliations

. 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.

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