Why do partitions occur in Faa di Bruno's chain rule for higher derivatives?

Details Why do partitions occur in Faa di Bruno's chain rule for higher derivatives? Why do partitions occur in Faa di Bruno's chain rule for higher derivatives?

2006-02-09

arxiv.org/abs/math/0602183v1

Mathematics

General Mathematics

10 pages

Scientific paper

It is well-known that the coefficients in Faa di Bruno's chain rule for higher derivatives can be expressed via numeration of partitions. It turns out that this has a natural form as a formula for the vector case. To this formula two proofs are presented, both "explaining" its form involving partitions: one as a purely algebraic fact, and one "from first principles" for the case of Frechet derivatives of mappings between Banach spaces.

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