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Comment by JoshTriplett | Hacker News Reader

This sounds fascinating! What was the structure, and what was the sequence?

I can't give any detail, but the solution to my problem involves k-variate k-nomial multinomial coefficients [1]. It's a generalization of the binomial coefficients to high-order scenarios such as trinomial coefficients, quadrinomial coefficients, etc. In other words, from a Pascal triangle to a Pascal pyramid, to a Pascal hyperpyramid.

[1] https://oeis.org/wiki/Multinomial_coefficients

Multinomial coefficients are also used to define the multinomial distribution in probability which models e.g. the problem of "if I throw a fair die n times, how likely is it that I get exactly x1 ones, x2 twos, ..., x6 sixes?" - which is a generalisation of the binomial distribution in which there are only two cases.

This is not "graduate-level", it's a straightforward generalization of something that all school age kids learn. (Which is not too say that it's trivial to obtain an expression. I'm just saying it's not conceptually advanced)

Per a nitty exploitable quote, do you have the slightest idea how little that narrows it down?

You can generalize addition to semigroups but that's not a point, eh?

That's like arguing all math is addition (it's just a bunch of sum signs), therefore all math is not actually graduate level. It's a straightforward generalization of something that all school kids learn.

Also, math achievement in America is horrible. 40% of students leave 12th grade at "Less than Basic". Only 2-3% leave 12th grade at "Advanced." Must not be very straightforward. (21% "Proficient", 35% "Basic" in 2019)

https://nces.ed.gov/programs/coe/indicator/cnc

Also, "The Distribution User Skills, Worse than You Think" https://news.ycombinator.com/item?id=36620608

It's not even just math. Over half of the US adult population reads below a sixth-grade level. Their science literacy is worse.

No details but it's related to Pascal triangles? So it involves pricing financial instruments, seems like a safe guess...

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