Timeline for Dimension of the span of all partial derivatives of a given homogeneous symmetric polynomial $f$ and the polynomial $E(f)$
Current License: CC BY-SA 4.0
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| Jul 5, 2020 at 14:20 | history | edited | Hector Blandin | CC BY-SA 4.0 |
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| Jun 2, 2015 at 16:21 | vote | accept | Hector Blandin | ||
| May 6, 2015 at 14:47 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 5, 2015 at 9:45 | answer | added | Christian Remling | timeline score: 2 | |
| May 5, 2015 at 0:42 | history | edited | Hector Blandin |
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| May 5, 2015 at 0:24 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 5, 2015 at 0:18 | comment | added | Pedro M. | Sorry, I had misunderstood the problem. | |
| May 5, 2015 at 0:13 | comment | added | Hector Blandin | No, because the dimension is 1, when $f=(x_1+\cdots+x_n)^d$. Since any partial derivative gives us $$ \frac{\partial f}{\partial x_i}=d\cdot (x_1+\cdots+x_n)^{d-1}. $$ and $E(f)=d(d-1)\cdot (x_1+\cdots+x_n)^{d-1}$ we see that the desired dimension is always 1. | |
| May 5, 2015 at 0:12 | review | Close votes | |||
| May 5, 2015 at 5:50 | |||||
| May 5, 2015 at 0:12 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 5, 2015 at 0:03 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 5, 2015 at 0:00 | comment | added | Hector Blandin | For more references and details please look at arxiv.org/abs/1504.07318 | |
| May 4, 2015 at 23:59 | comment | added | Pedro M. | This was also posted on Math.SE. Please indicate when you post in multiple forums. | |
| May 4, 2015 at 23:59 | comment | added | Hector Blandin | It comes from my PhD thesis | |
| May 4, 2015 at 23:57 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 4, 2015 at 23:56 | comment | added | Per Alexandersson | Can you please provide a bit more background? Where does this problem appear? | |
| May 4, 2015 at 23:56 | history | edited | Hector Blandin | CC BY-SA 3.0 |
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| May 4, 2015 at 23:52 | review | First posts | |||
| May 4, 2015 at 23:56 | |||||
| May 4, 2015 at 23:51 | history | asked | Hector Blandin | CC BY-SA 3.0 |