On knots with no 3-state

被引：1

作者：

Nakamura, Takuji ^{[1
]}

Nakanishi, Yasutaka ^{[2
]}

Satoh, Shin ^{[2
]}

机构：

[1] Osaka Electrocommun Univ, Dept Engn Sci, Neyagawa, Osaka 5728530, Japan

[2] Kobe Univ, Dept Math, Nada Ku, Kobe, Hyogo 6570013, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2015年 / 196卷

关键词：

State number; 3-State; Virtual knot; Gauss diagram; Miyazawa polynomial; n-Writhe; Upper group; Lower group; VIRTUAL KNOT;

D O I：

10.1016/j.topol.2015.05.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A state of a virtual knot diagram D is a disjoint union of circles obtained from D by splicing all real crossings. For each positive integer n, we denote by s(n)(D) the number of states of D consisting of n circles. The first aim of this paper is to characterize the virtual knot diagrams with s(3)(D) = 0 in terms of their Gauss diagrams. The 3-state number of a virtual knot K is defined to be the minimal number of s(3)(D) among all possible diagrams D for K. The second aim of this paper is to study several properties of the virtual knots with s(3)(K) = 0. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：754 / 770

页数：17

共 5 条

[1] The pole diagram and the Miyazawa polynomial [J].

Ishii, Atsushi .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2008, 19 (02) :193-207

[2] Virtual knot theory [J].

Kauffman, LH .

EUROPEAN JOURNAL OF COMBINATORICS, 1999, 20 (07) :663-690

[3] A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR VIRTUAL KNOTS AND LINKS [J].

Miyazawa, Yasuyuki .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2008, 17 (11) :1311-1326

[4] The state numbers of a virtual knot [J].

Nakamura, Takuji ;

Nakanishi, Yasutaka ;

Satoh, Shin ;

Tomiyama, Yumi .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2014, 23 (03)

[5] The writhes of a virtual knot [J].

Satoh, Shin ;

Taniguchi, Kenta .

FUNDAMENTA MATHEMATICAE, 2014, 225 :327-341

← 1 →