Timeline for maximizing multivariate polynomial
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 18, 2013 at 10:21 | comment | added | Turbo | @Noam Elkies I agree on the artofproblemsolving art. The reason I posted this was whether I could get any generic techniques to understand the higher dimensional version of this problem. The higher dimensional version of this problem at $N=7$ is exactly openproblemgarden.org/op/shannon_capacity_of_the_seven_cycle | |
| May 17, 2013 at 17:11 | comment | added | Noam D. Elkies | This seems more suitable for artofproblemsolving, but anyway: Since the polynomial is linear in each variable $y_i$ separately (once $N>2$), we may assume each $y_i \in \lbrace 0, 1 \rbrace$ (even if the intention was to just limit to the hypercube $0 \leq y_i \leq 1$. So we're just asking for the maximal number of 010 patterns in a cycle of $N+1$ zeros and ones. Since no two consecutive triples can be 010, the count is at most $\lfloor (N+1)/2 \rfloor$, and this is easily attained, and only by 010101... and its cyclic shifts (a total of $2$ if $N$ is even and $N+1$ if $N$ is odd). | |
| May 16, 2013 at 21:05 | answer | added | Yuandong | timeline score: 1 | |
| Dec 21, 2011 at 11:22 | comment | added | Igor Rivin | @Noah, this is for unknown to comment on, but it is all in the spin :) Anyway, no harm done, I am sure. | |
| Dec 21, 2011 at 1:55 | comment | added | Noah Stein | I intended no offense and so I apologize if any was taken. | |
| Dec 20, 2011 at 22:50 | answer | added | Igor Rivin | timeline score: 1 | |
| Dec 20, 2011 at 14:35 | comment | added | Igor Rivin | @Noah: this sort of comment can be summarized as: "I am smarter than you, nyah, nyah". If you want to give the OP a hint, by all means, but otherwise this is not appropriate. | |
| Dec 20, 2011 at 14:01 | comment | added | Noah Stein | Optimizing the given $J$ should not be thought of as a polynomial optimization problem, but rather a very simple combinatorial problem. As such it is not really appropriate for this site. The question of arbitrary $J$ is probably too general to get a good answer, especially since the given $J$ is poor motivation for it. If you're having trouble maximizing the given $J$, feel free to ask on math.stackexchange.com. | |
| Dec 20, 2011 at 4:29 | history | asked | Turbo | CC BY-SA 3.0 |