On combinatorial differential equations

DOI10.1016/0022-247X(86)90310-0zbMath0622.34013OpenAlexW2093914815MaRDI QIDQ1090823

Gilbert Labelle

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(86)90310-0

zbMATH Keywords

combinatorial speciesNewton-Raphson iterative schemefirst order initial value differential problemnon-isomorphic combinatorial solutions

Mathematics Subject Classification ID

General theory for ordinary differential equations (34A99) Numerical analysis in abstract spaces (65J99)

Related Items

Trees, arborescences, and symmetric square roots ⋮ On the generalized iterates of Yeh's combinatorial \({\mathbb{K}}\)-species ⋮ The relation between Burnside rings and combinatorial species ⋮ Combinatorial proofs of symmetry formulas for the generalized hypergeometric series ⋮ Differential 2-rigs ⋮ Combinatorial proofs of some limit formulas involving orthogonal polynomials ⋮ Algorithms for combinatorial structures: well-founded systems and Newton iterations ⋮ Free integro-differential algebras and Gröbner-Shirshov bases. ⋮ The Combinatorics of Laguerre, Charlier, and Hermite Polynomials ⋮ On asymmetric structures ⋮ Combinatorial functional and differential equations applied to differential posets ⋮ The equations \(D^ k Y = X^ n\) in combinatorial species ⋮ Counting asymmetric enriched trees ⋮ On the symmetry and asymmetry of combinatorial structures ⋮ The adjoints to the derivative functor on species ⋮ Families of combinatorial solutions of \(y\prime = 1 + y^ 2\) and autonomous differential equations ⋮ Dérivées directionnelles et développements de Taylor combinatoires. (Directional derivatives and combinatorial Taylor expansions)

Uses Software

• Cayley
• MACSYMA

Cites Work

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• Une approche combinatoire pour l'itération de Newton-Raphson
• Éclosions combinatoires appliquées à l'inversion multidimensionnelle des séries formelles. (Combinatorial bloomings applied to the multidimensional inversion of formal series)
• Une combinatoire sous-jacente au théorème des fonctions implicites. (Combinatorics underlying the implicit functions theorem)
• Une interpretation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi
• Differentiably finite power series
• Une nouvelle demonstration combinatoire des formules d'inversion de Lagrange
• Une approche combinatoire des fonctions elliptiques de Jacobi
• Une théorie combinatoire des séries formelles
• A combinatorial application of matrix Riccati equations and their q- analogue
• A method and two algorithms on the theory of partitions
• Parallel concepts in graph theory
• The Hammond Series of a Symmetric Function and Its Application to P-Recursiveness
• The transitive groups of degree up to eleven⁺
• Computers in group theory

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