We bring cocycle enhancement theory to the case of psyquandles. Analogously to our previous work on virtual biquandle cocycle enhancements, we define enhancements of the psyquandle counting invariant via pairs of a biquandle 2-cocycle and a new function satisfying some conditions. As an application we define new single-variable and two-variable polynomial invariants of oriented pseudoknots and singular knots and links. We provide examples to show that the new invariants are proper enhancements of the counting invariant and are not determined by the Jablan polynomial.

中文翻译：

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psyquandle 计数不变量的 Cocycle 增强

我们将 cocycle 增强理论带到了 psyquandles 的案例中。类似于我们之前关于虚拟双组共循环增强的工作，我们通过成对的双组 2-共循环和满足某些条件的新函数来定义 psyquandle 计数不变量的增强。作为一个应用程序，我们定义了定向伪结和奇异结和链接的新的单变量和二变量多项式不变量。我们提供了例子来说明新的不变量是计数不变量的适当增强，并且不是由 Jablan 多项式确定的。