Unsurprisingly(?) often, Cartesian products and general exhaustive combinatorial enumeration is pretty great
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my retirement project is enumerative combinatorics and theory of partitions. Those texts have been sitting on my bookshelf for 25 years at this point. Used them a little in grad school, but never got a chance to go deep, since the subject is owned by genius number theorists
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Are they not owned by (enumerative) combinatorialists? I think parititions come up a little in NT but I feel most combinatorics in number theory is extremal and not enumerative
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Broad strokes... it's the same kind of brain that is good at both (I'm talking closed form, series expansions, etc etc). There's a fair overlap in basic techniques I think.
More broadly... the presence of genius-type people driving both makes it hard for very mediocre math people like me to get in the game or keep up in a context like grad school where you actually have to be good enough to play. Retirement standards I can dabble at amateur level
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I think of this as where the analysis techs come in and mesh with combinatorics, so that would explain why you’d think number theory.
I guess I find the two types of brains to be quite different, but it’s one of those “magnifying diffs from POV of someone too close” thing.😂
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