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.
Linares, Insertion pre-Lie products and translation of rough paths based on multi-indices, preprint
3 Pith papers cite this work. Polarity classification is still indexing.
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Explicit formulas, functional equations, and recursions are given for the cardinalities of fertility fibres of decorated trees, along with coefficient generating functions that refine the admissible-cut coproduct in the LOT Hopf algebra.
Computes dimensions of symmetry spaces for the gKPZ equation via multi-indices that avoid over-parametrization, providing an elementary proof that simplifies prior decorated-tree results and completes the chain-rule program.
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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.
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Fertility fibres and coproduct coefficients in the LOT Hopf algebra
Explicit formulas, functional equations, and recursions are given for the cardinalities of fertility fibres of decorated trees, along with coefficient generating functions that refine the admissible-cut coproduct in the LOT Hopf algebra.
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Symmetries for the gKPZ equation via multi-indices
Computes dimensions of symmetry spaces for the gKPZ equation via multi-indices that avoid over-parametrization, providing an elementary proof that simplifies prior decorated-tree results and completes the chain-rule program.