On arrow polynomials of checkerboard colorable virtual links-Reference-Cited by-同舟云学术

On arrow polynomials of checkerboard colorable virtual links

Published:2021-06 Issue:07 Volume:30 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Deng Qingying¹,Jin Xian’an²,Kauffman Louis H.³

Affiliation:

1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China

2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China

3. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA

Abstract

In this paper, we give two new criteria of detecting the checkerboard colorability of virtual links by using the odd writhe and the arrow polynomial of virtual links, respectively. As a result, we prove that 6 virtual knots are not checkerboard colorable, leaving only one virtual knot whose checkerboard colorability is unknown among all virtual knots up to four classical crossings.

Funder

National Natural Science Foundation of China

Fundamental Research Funds for Central Universities of the Central South University

Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai

Doctor's Funds of Xiangtan University

the Laboratory of Topology and Dynamics, Novosibirsk State University

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821652150053X