

Generating functions and counting - guffshemr
http://berezecki.com/?p=40

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dododo
i read some of this book (analytic combinatorics). it's quite nice in that if
you can write down something akin to a grammar that constructs objects you
want to count, it provides a set of rewrite rules to actually count them.
unfortunately it doesn't provide a way to count anything more complex
recursively than a tree that i could see.

for understanding the tree results, the key thing to understand appears to be
lagrange's inversion theorem:
<http://en.wikipedia.org/wiki/Lagrange_inversion_theorem> (i think it's also
in an appendix in the book)

an interesting connection between probability/ai and this: the probability
generating function is a normalized form of these generating functions that
allows you to specify a probability distribution:
<http://en.wikipedia.org/wiki/Probability_generating_function>

in particular, you can use this to work out the average size of a tree picked
at random :-)

------
carterschonwald
for those who'd like to learn more about generating functions, one of the best
books on such, generatingfunctionology by wilf, is available as a free pdf
online at www.math.upenn.edu/~wilf/DownldGF.html

~~~
jimmyjim
I would love to get a hold of that book, but it seems to be unavailable from
your link. I cannot find it anywhere else, would you happen to have another
link? If you have it yourself, could you please upload it?

~~~
TY
Here is the direct link to the PDF version of the second edition published in
1994 (third one published in 2006 is in print though):

<http://www.math.upenn.edu/~wilf/gfology2.pdf>

