4 ms·

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 coeffici

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 https://oeis.org/wiki/Multinomial_coefficients

Tainnor 3y ago
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.
bdjsiqoocwk 3y ago
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)
- deruta 3y ago
  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?
- araes 3y ago
  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 https://nces.ed.gov/programs/coe/indicator/cnc Also, "The Distribution User Skills, Worse than You Think" https://news.ycombinator.com/item?id=36620608 https://news.ycombinator.com/item?id=36620608
  - autoexec 3y ago
    It's not even just math. Over half of the US adult population reads below a sixth-grade level. Their science literacy is worse.
gwern 3y ago
No details but it's related to Pascal triangles? So it involves pricing financial instruments, seems like a safe guess...

Tainnor 3y ago

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.

bdjsiqoocwk 3y ago

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)

deruta 3y ago
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?
araes 3y ago
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 https://nces.ed.gov/programs/coe/indicator/cnc Also, "The Distribution User Skills, Worse than You Think" https://news.ycombinator.com/item?id=36620608 https://news.ycombinator.com/item?id=36620608
- autoexec 3y ago
  It's not even just math. Over half of the US adult population reads below a sixth-grade level. Their science literacy is worse.

gwern 3y ago

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