Timeline for Polynomial defined recursively by a resultant
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2019 at 5:08 | comment | added | Per Alexandersson | @Hellbound I have typed up some basic properties + examples on my web page: math.upenn.edu/~peal/polynomials/plethysm.htm There is also references there for additional sources. | |
| Sep 17, 2019 at 4:00 | comment | added | PalmTopTigerMO | @PerAlexandersson Can you recommend a good introductary material for plethysm? | |
| Sep 16, 2019 at 13:47 | comment | added | Per Alexandersson | There could perhaps be worth looking at plethysm... | |
| Sep 16, 2019 at 11:11 | answer | added | Norman Wildberger | timeline score: 3 | |
| Jul 29, 2019 at 20:34 | history | edited | PalmTopTigerMO | CC BY-SA 4.0 |
added 550 characters in body
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| Jul 28, 2019 at 20:34 | comment | added | PalmTopTigerMO | @YCor I see your point, and chose to edit my question accordingly. Thank you | |
| Jul 28, 2019 at 20:32 | history | edited | PalmTopTigerMO | CC BY-SA 4.0 |
added 73 characters in body
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| Jul 28, 2019 at 17:34 | comment | added | YCor | It's a matter of presentation: it may be easier indeed to write an obviously well-defined recursive definition, and then observe that the resulting sequence satisfies other recursive properties, rather than making the definition itself depend on some lemma (which requires some attention to be convinced of). | |
| Jul 28, 2019 at 17:12 | comment | added | PalmTopTigerMO | @YCor Of course, it is true that if $4 \le n$ then $P_{n}=Res_{\mathbf{x}}\left(P_{3}\left(x_1,x_2,\mathbf{x} \right),P_{n-1}\left(x_3,x_4,...,x_{n},\mathbf{x} \right) \right)$, which may be more simple. | |
| Jul 28, 2019 at 11:08 | comment | added | PalmTopTigerMO | @YCor Indeed. You might say that the recursive step is defined by a 2-partition of $n+2$, where each part is equal or greater than $3$. This is well defined due to the properties of the resultant and the fact that the base case is a symmetric polynomial. | |
| Jul 28, 2019 at 9:42 | comment | added | YCor | "where $n_0,n_1\ge 3$ and $n_0+n_1=n+2$": do you mean this does not depend on such a choice of $n_0,n_1$? | |
| Jul 28, 2019 at 9:41 | history | edited | YCor | CC BY-SA 4.0 |
deleted 14 characters in body; edited tags; edited title
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| Jul 28, 2019 at 8:38 | comment | added | PalmTopTigerMO | @GerryMyerson The last edit fixes the issue. The original can still be seen in the MSE post at the head of this question. Thank you | |
| Jul 28, 2019 at 8:35 | history | edited | PalmTopTigerMO | CC BY-SA 4.0 |
Changed the indices of $P_{n_1}$ in the recursive definition to be more compact, so what's to the right of the "if"s is not obscured. Original can still be seen on the MSE post
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| Jul 28, 2019 at 6:13 | comment | added | Gerry Myerson | Everything to the right of the "if"s in the first display gets hidden underneath the block headed "Blog". Could you/someone edit the display so it doesn't extend so far to the right? | |
| Jul 27, 2019 at 16:40 | history | asked | PalmTopTigerMO | CC BY-SA 4.0 |