Research ArticleNo Access

On arrow polynomials of checkerboard colorable virtual links

Qingying Deng

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

E-mail Address: qingying@xtu.edu.cn

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Xian’an Jin

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

E-mail Address: xajin@xmu.edu.cn

Corresponding author.

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, and

Louis H. Kauffman

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

E-mail Address: loukau@gmail.com

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https://doi.org/10.1142/S021821652150053XCited by:1 (Source: Crossref)

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.

Keywords:

AMSC: 57K14, 57K12, 57K10

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