A note on the writhe polynomial and the virtual crossing number

TL;DR

This paper introduces a refined lower bound on the virtual crossing number using the writhe polynomial, offering a new interpretation and characterization of the polynomial to improve understanding in virtual knot theory.

Contribution

It provides a novel lower bound on the virtual crossing number based on a new interpretation of the writhe polynomial, refining previous results.

Findings

New lower bound on virtual crossing number

Refined interpretation of the writhe polynomial

Discussion on characterization of the writhe polynomial

Abstract

In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of the writhe polynomial. The characterization of the writhe polynomial is also discussed.