A combinatorial view of Holant problems on higher domains
<|reference_start|>A combinatorial view of Holant problems on higher domains: 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.<|reference_end|>
@article{liu2024a,
    title={A combinatorial view of Holant problems on higher domains},
    author={Yin Liu},
    journal={arXiv preprint arXiv:2403.14150},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14150},
    primaryClass={cs.CC math.CO}
}