Timeline for Number of degree $k$ functions [closed]
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18 events
| when toggle format | what | by | license | comment | |
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| Jan 15, 2015 at 3:21 | history | edited | Turbo | CC BY-SA 3.0 |
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| Jan 14, 2015 at 22:05 | comment | added | Emil Jeřábek | (1) Not $2^{n/2}$, but a $2^{-n/2}$ fraction. More precisely, the number of functions of degree $< n$ is $\binom{2^n}{2^{n-1}}$ because of cstheory.stackexchange.com/a/27048 . (2) As I already wrote, I’m skeptical. We are talking an intersection of a linear space with a discrete set. | |
| Jan 14, 2015 at 18:42 | review | Reopen votes | |||
| Jan 15, 2015 at 10:24 | |||||
| Jan 14, 2015 at 18:26 | comment | added | Turbo | @EmilJeřábek $(1)$ How did you get count $2^{\frac{n}{2}}$? $(2)$ Is there a linear algebra technique as mentioned in a comment above? | |
| Jan 14, 2015 at 13:46 | comment | added | Emil Jeřábek | I don’t think it’s easy over the reals, and there likely isn’t any decent exact expression except for a few special cases. Though it’s easy to see that all but a tiny fraction ($\approx2^{-n/2}$) of all functions have degree $n$. | |
| Jan 14, 2015 at 8:11 | comment | added | Turbo | I am getting not much help here math.stackexchange.com/questions/1103587/…? | |
| Jan 14, 2015 at 8:10 | history | undeleted | Turbo | ||
| Jan 14, 2015 at 4:07 | history | deleted | Turbo | via Vote | |
| Jan 14, 2015 at 4:07 | history | undeleted | Turbo | ||
| Jan 14, 2015 at 4:06 | history | deleted | Turbo | via Vote | |
| Jan 14, 2015 at 1:50 | history | closed |
Emil Jeřábek Stefan Kohl♦ Ryan Budney S. Carnahan♦ |
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| Jan 14, 2015 at 1:50 | comment | added | S. Carnahan♦ | This is elementary linear algebra. Why are you asking this on a research mathematics site? | |
| Jan 13, 2015 at 18:59 | history | edited | Turbo | CC BY-SA 3.0 |
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| Jan 13, 2015 at 18:59 | comment | added | Turbo | I am talking about reals. | |
| Jan 13, 2015 at 13:31 | comment | added | Emil Jeřábek | Or are you talking about a different field than $\mathbb F_2$, by any chance? Then you need to make that explicit in the question. | |
| Jan 13, 2015 at 12:46 | review | Close votes | |||
| Jan 14, 2015 at 1:53 | |||||
| Jan 13, 2015 at 12:31 | comment | added | Emil Jeřábek | How many degree $\le k$ multilinear monomials in $n$ variables are there? This is trivial combinatorics. | |
| Jan 13, 2015 at 8:20 | history | asked | Turbo | CC BY-SA 3.0 |