The state numbers of a virtual knot

作者：Nakamura Takuji^*; Nakanishi Yasutaka; Satoh Shin; Tomiyama Yumi

来源：Journal of Knot Theory and Its Ramifications, 2014, 23(3): 1450016.

DOI：10.1142/S0218216514500163

• State number
• virtual knot
• Gauss diagram
• Jones polynomial
• Miyazawa polynomial

A state of a virtual knot diagram D is a disjoint union of circles obtained from D by splicing all real crossings. For each integer n > 0, we denote by s(n)(D) the number of states of D consisting of n circles. The state number of a virtual knot K is the minimal number of s(n)(D) for all diagrams D of K and denoted by s(n)(K). The aim of this paper is to study s(n)(D) and sn(K).

• 出版日期2014-3