We introduce \textit{Kaestner brackets}, a generalization of biquandle brackets to the case of parity biquandles. This infinite set of quantum enhancements of the biquandle counting invariant for oriented virtual knots and links includes the classical quantum invariants, the quandle and biquandle $2$-cocycle invariants and the classical biquandle brackets as special cases, coinciding with them for oriented classical knots and links but defining generally stronger invariants for oriented virtual knots and links. We provide examples to illustrate the computation of the new invariant and to show that it is stronger than the classical biquandle bracket invariant for virtual knots.

中文翻译：

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凯斯特纳括号

我们介绍了 \textit{Kaestner 括号}，这是对奇偶双方括号情况的双四方括号的推广。用于定向虚拟结和链接的双群数计数不变量的无限量子增强集包括经典量子不变量、quandle 和 biquandle $2$-cocycle 不变量以及作为特殊情况的经典双量子括号，它们与定向经典结和链接一致但通常为定向虚拟节点和链接定义更强的不变量。我们提供了一些例子来说明新不变量的计算，并表明它比虚拟结的经典双四方括号不变量更强。