Fa di Bruno's formula, lattices, and partitions
The coefficients of g(s) g ( s ) in expanding the r th derivative of the composite function g?f g ? f by Fa 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.
primary 11d04 secondary 05a17 11d45 11y50 15a36 68r05