文档介绍：generatingfunctionology
Herbert S. Wilf
Department of Mathematics
University of Pennsylvania
Philadelphia, Pennsylvania
Copyright 1990 and 1994 by Academic Press, Inc. All rights re-
served. This Edition may be reproduced for any valid educational
purpose of an institution of higher learning, in which case only the reason-
able costs of reproduction may be charged. Reproduction for profit or for
mercial purposes is strictly prohibited.
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Preface
This book is about generating functions and some of their uses in
discrete mathematics. The subject is so vast that I have not attempted to
give prehensive discussion. Instead I have tried only municate
some of the main ideas.
Generating functions are a bridge between discrete mathematics, on
the one hand, and continuous analysis (plex variable the-
ory) on the other. It is possible to study them solely as tools for solving
discrete problems. As such there is much that is powerful and magical in
the way generating functions give unified methods for handling such prob-
lems. The reader who wished to omit the analytical parts of the subject
would skip chapter 5 and portions of the earlier material.
To omit those parts of the subject, however, is like listening to a stereo
broadcast of, say, Beethoven’s Ninth Symphony, using only the left audio
channel.
The full beauty of the subject of generating functions emerges only
from tuning in on both channels: the discrete and the continuous. See
how they make the solution of difference equations into child’s play. Then
see how the theory of functions of plex variable gives, virtually by
inspection, the approximate size of the solution. The interplay between the
two channels is vitally important for the appreciation of the music.
In recent years there has been a vigorous trend in the direction of
finding bijective proofs binatorial theorems. That is, if we want to
prove that two sets have the same cardinality then we should be able to
do it b