3 problems

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Highest- $x$ coefficient conjecture for refined partition generating functions
Highest- $x$ coefficient conjecture. For generic genus $g>0$ ,
Conjectureopengenerating-functions genus-enumeration set-partitionsarXiv posted 2 days ago
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Formula for the first nontrivial numerator coefficient of genus-dependent Bell generating functions
Numerator-coefficient conjecture. The first nontrivial coefficient of $P^{(g)}(x)$ is divisible by $6$ , and after division by $6$ the resulting sequence is
Conjectureopengenerating-functions genus-enumerationarXiv posted 2 days ago
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Genus-three Bell-number formula and genus-dependent generating-function ansatz
Genus-three Bell-number and generating-function conjecture. The genus-three numbers satisfy
Conjectureopengenerating-functions genus-enumeration set-partitionsarXiv posted 2 days ago

Highest-xxx coefficient conjecture for refined partition generating functions