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Borwein, J. M.; Crandall, R. E.: Closed Forms: What They Are and Why We Care. Notices of the AMS 60 (2013) (1) 50-65 http://mathworld.wolfram.com/Closed-FormSolution.html https://en.wikipedia.org/wiki/Closed-form_expression https://www.encyclopediaofmath.org/index.php/Integration_of_differential_equations_in_closed_form  Shackell, J. R.: Symbolic ...

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I am fairly certain this is false in general (although it works for certain special $S$ and might work for small values of $d$, but when $d$ is sufficiently large relative to $k=|V(S)|$ it shouldn't work). Here's why, and some reasoning that might help you characterize exactly for which $S$ it works. Fix $S$, and let $s(G)$ denote the number of copies of $S$...

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I apologize in advance for my abuse of set notation as I am mapping one mathematical object that is not quite a set i.e. graphs to another mathematical object that is not quite a set i.e. sequences. Feel free to comment or correct notation etc. Definitions: (1) The triangular-harmonic numbers $\Theta$ are a monotonic sequence of rational numbers greater ...

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