Montesinos 纽结的 Delta-解纽数
Delta-Unknotting Number for Montesinos Knots
浏览论文内容
中文总结 AI 辅助
本文确定了特定 Montesinos 纽结族的 Delta-解纽数，证明其等于 Conway 多项式第二系数的绝对值，涵盖所有正 pretzel 纽结及部分双桥纽结。
中文摘要 AI 辅助
纽结的 $\Delta$-解纽数定义为将该纽结变形为平凡纽结所需的最少 $\Delta$-移动次数。本文确定了某些 Montesinos 纽结族的 $\Delta$-解纽数。利用关于 pretzel 纽结和双桥纽结的结果，我们证明对于这些纽结族，$\Delta$-解纽数等于 Conway 多项式第二系数的绝对值。特别地，每个正 pretzel 纽结都属于这些族，某些双桥纽结也属于这些族。
英文摘要
The $Δ$-unknotting number for a knot is defined as the minimum number of $Δ$-moves needed to deform the knot into the trivial knot. In this paper, we determine the $Δ$-unknotting numbers for certain families of Montesinos knots. Using results on pretzel knots and two-bridge knots, we prove that for these families the $Δ$-unknotting number equals the absolute value of the second coefficient of the Conway polynomial. In particular, every positive pretzel knot belongs to these families, and certain two-bridge knots also belong to them.
