论文信息 - Faa' di Bruno's formula, lattices, and partitions

Faa' di Bruno's formula, lattices, and partitions

The coefficients of g(s) in expanding the rth derivative of the composite function g ○ f by Faa di Bruno's formula, is determined by a Diophantine linear system, which is proved to be equivalent to the problem of enumerating partitions of a finite set of integers attached to r and s canonically.

Ángel Martín del Rey | Jaime Muñoz Masqué | Luis Hernández Encinas

[1] G. Constantine. Combinatorial theory and statistical design , 1987 .

[2] Doron Zeilberger,et al. Kathy O'Hara's constructive proof of the unimodality of the Gaussian polynomials , 1989 .

[3] K. Aardal. Solving a System of Diophantine Equations with Lower and Upper Bounds on the Variables , 1998 .

[4] L. Fraenkel. Formulae for high derivatives of composite functions , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] Masaki Kawagishi,et al. The multi-dimensional Faa di Bruno formula , 1999 .

[6] Arjen K. Lenstra,et al. Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables , 2000, Math. Oper. Res..

[7] Joachim von zur Gathen,et al. Modern Computer Algebra , 1998 .

[8] Winston C. Yang. Derivatives are essentially integer partitions , 2000, Discret. Math..

[9] Ellis Horowitz,et al. Computing Partitions with Applications to the Knapsack Problem , 1974, JACM.

[10] J. Langley,et al. ON THE DERIVATIVES OF COMPOSITE FUNCTIONS , 2007 .

[11] G. Constantine,et al. A Multivariate Faa di Bruno Formula with Applications , 1996 .

[12] Rumen L. Mishkov,et al. Generalization of the formula of Faa di Bruno for a composite function with a vector argument , 2000 .

[13] Harley Flanders,et al. From Ford to Faà , 2001, Am. Math. Mon..