Unsurprisingly(?) often, Cartesian products and general exhaustive combinatorial enumeration is pretty greathttps://twitter.com/krzhang/status/1268986931079024645 …
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It's a (seductive) trap!
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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.
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