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Any general tips on or examples of finding interesting generating functions from recurrence relations involving minimization and maximization?

I'd imagine the case with one term of a minimization or maximization being constant is already interesting, presumably that covers pricing American style options, although no solution has jumped out at me yet.

I'm most curious about interesting generating functions for recurrences involving minimization or maximization over multiple non-constant but not terribly complex terms however.

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Jeff- This is isn't my area, so I can't judge questions very well, but this seems like an exceptionally vague question. Do you have a particular such generating function you're interested in? As it stands, I suspect this question will be closed, so I recommend you make it a bit more specific. The how-to-ask might be helpful: mathoverflow.net/howtoask –  Ben Webster Apr 11 '11 at 1:09
What Ben said. Even one example of a recurrence relation involving minimization would be helpful. You might find something in the Graham-Knuth-Ptashnik book, Concrete Mathematics. –  Gerry Myerson Apr 11 '11 at 2:13
What would a good answer to this question look like? What would you do with it? Gerhard "Ask Me About System Design" Paseman, 2011.04.10 –  Gerhard Paseman Apr 11 '11 at 4:24
Maybe a better reference than GKP is Greene, Mathematics for the Analysis of Algorithms, section 2.2.1. –  Gerry Myerson Apr 11 '11 at 6:08
Thanks Gerry! Greene has a sufficiently general example. –  Jeff Burdges Apr 12 '11 at 11:41
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