On the B-series composition theorem
<|reference_start|>On the B-series composition theorem: The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in B-series analysis favour the use of unlabelled trees. In this paper, we present a new proof of the B-series composition theorem that does not depend on labelled trees. A key challenge in this approach is accurately counting combinations related to ``pruning.'' This challenge is overcome by introducing the concept of ``assignment.''<|reference_end|>
@article{butcher2024on,
    title={On the B-series composition theorem},
    author={John C. Butcher, Taketomo Mitsui, Yuto Miyatake, Shun Sato},
    journal={arXiv preprint arXiv:2409.08533},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08533},
    primaryClass={math.NA cs.NA}
}