2021 年 73 巻 3 号 p. 983-994
Satoh and Taniguchi introduced the 𝑛-writhe 𝐽𝑛 for each non-zero integer 𝑛, which is an integer invariant for virtual knots. The sequence of 𝑛-writhes {𝐽𝑛}𝑛 ≠ 0 of a virtual knot 𝐾 satisfies ∑𝑛 ≠ 0 𝑛𝐽𝑛(𝐾) = 0. They showed that for any sequence of integers {𝑐𝑛}𝑛 ≠ 0 with ∑𝑛 ≠ 0 𝑛𝑐𝑛 = 0, there exists a virtual knot 𝐾 with 𝐽𝑛(𝐾) = 𝑐𝑛 for any 𝑛 ≠ 0. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. The unknotting number by the virtualization is called the virtual unknotting number and is denoted by 𝑢𝑣. In this paper, we show that if {𝑐𝑛}𝑛 ≠ 0 is a sequence of integers with ∑𝑛 ≠ 0 𝑛𝑐𝑛 = 0, then there exists a virtual knot 𝐾 such that 𝑢𝑣(𝐾) = 1 and 𝐽𝑛(𝐾) = 𝑐𝑛 for any 𝑛 ≠ 0.
この記事は最新の被引用情報を取得できません。