Pretzel 结的 Delta-解结数
Delta-Unknotting Number for Pretzel Knots
AI总结：
本文计算了正 pretzel 结的 Δ-解结数，并给出了奇型正 pretzel 结和环面结的最大值，以及特定负型 pretzel 结的 Δ-解结数。
摘要：
一个结的 $Δ$-解结数定义为将该结变形为平凡结所需的最少 $Δ$-移动次数。已知对于正 pretzel 结，$Δ$-解结数等于其 Conway 多项式的第二系数。本文计算了正 pretzel 结的 $Δ$-解结数。作为上述结果的一个推论，在具有固定交叉数 $n$（$n$ 为奇数）的奇型正 pretzel 结中，$Δ$-解结数由 $P(1, 1, ... , 1) \quad ig( \cong T(2,n) ig)$ 取最大值，最大值为 $ rac{1}{8}(n^2 - 1)$。我们还得到了环面结的类似结果。进一步地，我们确定了形如 $P(-1, p_2, ..., p_n)$ 的 pretzel 结的 $Δ$-解结数，其中 $2 \leq i \leq n$ 时 $p_i$ 为正奇数，且 $n$ 为奇数。
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. It is known that, for positive pretzel knots, the $Δ$-unknotting number coincides with the second coefficient of their Conway polynomial. In this paper, we compute the $Δ$-unknotting number for positive pretzel knots. As a consequence of the above result, among positive pretzel knots of odd type with a fixed crossing number $n$, where $n$ is odd, the $Δ$-unknotting number is maximized by $P(1, 1, ... , 1) \quad \big( \cong T(2,n) \big)$, and the maximum value is $\frac{1}{8}(n^2 - 1)$. We also obtain a similar result for torus knots. We further determine the $Δ$-unknotting number for pretzel knots of type $P(-1, p_2, ..., p_n)$, where $p_i$ is a positive odd integer for $2 \leq i \leq n$ and $n$ is odd.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
