Unsurprisingly(?) often, Cartesian products and general exhaustive combinatorial enumeration is pretty greathttps://twitter.com/krzhang/status/1268986931079024645 …
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Replying to @meditationstuff
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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Replying to @vgr @meditationstuff
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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Replying to @krzhang @meditationstuff
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.
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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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Replying to @vgr @meditationstuff
Yeah I think combinatorics would be particularly fun for you at the amateur level because of how much you can do with just a couple of books. It’s one field where people had a lot of success getting minorities (whatever metric) involved since the show-of-value is very fast
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I wouldn’t do partitions at that time tbh. Lots of more rewarding subfields / books! (Generating functions, transfer matrix method, Catalan numbers, beautiful statistical mechanics models, designs...)
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yeah... I used a couple of minor ideas, but frankly found the field pretty intimidating
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that's my secret cap; meta^n is just meta^1 for all levels of meta
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End of conversation
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