判定一个投影是否可分解为给定链环：线性时间算法
Deciding if a shadow resolves into a given link: linear-time algorithms
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中文总结 AI 辅助
该研究针对特定链环，提出线性时间算法以判定输入阴影是否可分解为该链环，明确了适用链环的范围。
中文摘要 AI 辅助
一个“阴影”（或称“投影”）是通过忽略链环图每个交叉点的上下信息得到的。给定固定链环L，我们研究判定输入阴影S是否可分解为L的复杂度，即能否为其交叉点分配上下信息以得到与L同痕的链环图。我们证明，若L属于{3₁,4₁,5₁,5₂,6₂,L2a1,L4a1,L5a1,L6n1}，则存在线性时间算法判定输入阴影S是否可分解为L。
英文摘要
A {\em shadow} (or {\em projection}) is obtained from a link diagram by ignoring the over/under information at each crossing. Given a fixed link $L$ we investigate the complexity of deciding whether an input shadow $S$ can be {\em resolved} into $L$, that is, whether we can assign over/under information to its crossings to obtain a diagram of a link isotopic to $L$. We show that if $L\in\{3_1,4_1,5_1,5_2,6_2,L2a1, L4a1, L5a1, L6n1\}$ then there exists a linear-time algorithm that decides whether an input shadow $S$ resolves into $L$.
