On the Boolean domain, there is a class of symmetric signatures called ``Fibonacci gates'' for which a beautiful P-time combinatorial algorithm has been designed for the corresponding $\operatorname{Holant}$ problems. In this work, I give a combinatorial view for $\operatorname{Holant}(\mathcal{F})$ problems on a domain of size 3 where $\mathcal{F}$ is a set of arity 3 functions with inputs taking values on the domain of size 3 and the functions share some common properties. The combinatorial view can also be extended to the domain of size 4. Specifically, I extend the definition of "Fibonacci gates" to the domain of size 3 and the domain of size 4. Moreover, I give the corresponding combinatorial algorithms.

翻译：在布尔域上，存在一类称为"斐波那契门"的对称签名，针对相应的$\operatorname{Holant}$问题已设计出优美的多项式时间组合算法。本工作中，针对定义在大小为3的域上的$\operatorname{Holant}(\mathcal{F})$问题，我提出了一种组合视角，其中$\mathcal{F}$是输入值取自大小为3的域的三元函数集合，且这些函数具有某些共同性质。该组合视角可进一步推广至大小为4的域。具体而言，我将"斐波那契门"的定义扩展至大小为3和大小为4的域，并给出了相应的组合算法。