Introduction to Combinatorial Analysis by John Riordan

Author:John Riordan
Language: eng
Format: epub
Publisher: Dover Publications

and

On the other hand, the same substitution of variables carries the power sum symmetric functions sl, s2, · · · defined by

into

Hence the relation between these two kinds of symmetric functions is a partial-fraction expansion for denumerant generating functions. As has already appeared in Problem 2.27,

or

where Yk is a Bell polynomial and Ck is the cycle indicator of Chapter 4.

The first instances of this relation, namely,

correspond to

(the last expression by use of the first). From these it is found that

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