By considering unknotting operations, we obtain ways of measuring how knotted a knot is. Unknotting phenomena can be seen not only in knot theory, but also in various settings such as DNA knots, mind knots and so on ([C. C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (American Mathematical Society, Providence, RI, 2004); A. Kawauchi, K. Kishimoto and A. Shimizu, Knot theory and game (in Japanese) (Asakura Publishing, Tokyo, 2013); L. Rudolph, Qualitative Mathematics for the Social Sciences (Routledge, London, 2013); K. Murasugi, Knot Theory and Its Applications, Translated from the 1993 Japanese original by Bohdan Kupita (Birkhauser, Boston, MA, 1996)], etc.). In this paper, we see how knots can be unknotted (and therefore how they are knotted) by considering various unknotting operations and their associated unknotting numbers.

中文翻译：

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对结和链接进行解结操作

通过考虑解结操作，我们获得了测量结的打结程度的方法。解结现象不仅可以在结理论中看到，还可以在 DNA 结、心灵结等各种设置中看到（[C. C. Adams,结书：结的数学理论入门（美国数学会，普罗维登斯，罗德岛州，2004 年）；A. Kawauchi、K. Kishimoto 和 A. Shimizu，结理论与博弈（日文）（朝仓出版社，东京，2013 年）；L.鲁道夫，社会科学的定性数学（劳特利奇，伦敦，2013 年）；K.村杉，结理论及其应用, 翻译自 Bohdan Kupita (Birkhauser, Boston, MA, 1996)] 等的 1993 年日文原版。在本文中，我们通过考虑各种解开操作及其相关的解开数来了解如何解开结（以及如何打结）。