Faà di Bruno's formula, lattices, and partitions

Authors:
L. Hernández Encinas;A. Martín del Rey;J. Muñoz Masqué
Affiliations:
Instituto de Física Aplicada, CSIC, Madrid, Spain;Departamento de Matemética Aplicada, E.P.S., Universidad de Salamanca, Ávila, Spain;Instituto de Física Aplicada, CSIC, Madrid, Spain
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

The coefficients of g(s) in expanding the rth derivative of the composite function g ○ f by Faà 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.