Term rewriting on nestohedra
<|reference_start|>Term rewriting on nestohedra: We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated poset on vertices generalizes Barnard--McConville's flip order for graph-associahedra, the preorder on faces likely generalizes the facial weak order for permutahedra. Moreover, we define and study contextual families of nestohedra, whose local confluence diagrams satisfy a certain uniformity condition. Among them are associahedra and operahedra, whose associated proofs of confluence for their rewriting systems reproduce proofs of categorical coherence theorems for monoidal categories and categorified operads.<|reference_end|>
@article{curien2024term,
    title={Term rewriting on nestohedra},
    author={Pierre-Louis Curien and Guillaume Laplante-Anfossi},
    journal={arXiv preprint arXiv:2403.15987},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15987},
    primaryClass={math.CT cs.LO math.AT math.CO}
}