Planar aromatic trees form the free tracial post-Lie-Rinehart algebra and yield new high-order divergence-free Lie-group numerical methods.
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Aromatic and clumped multi-indices are equipped with pre-Lie-Rinehart algebra, Hopf algebroid, and Hopf algebra structures to reduce volume-preservation studies to one dimension and generalize Hopf embeddings for numerical analysis.
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The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods
Planar aromatic trees form the free tracial post-Lie-Rinehart algebra and yield new high-order divergence-free Lie-group numerical methods.
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Aromatic and clumped multi-indices: algebraic structure and Hopf embeddings
Aromatic and clumped multi-indices are equipped with pre-Lie-Rinehart algebra, Hopf algebroid, and Hopf algebra structures to reduce volume-preservation studies to one dimension and generalize Hopf embeddings for numerical analysis.