Timeline for Prove or disprove that the power of positive term polynomial will be eventually single peak
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2022 at 1:22 | vote | accept | JetfiRex | ||
| Mar 13, 2022 at 0:13 | answer | added | David Handelman | timeline score: 8 | |
| Mar 11, 2022 at 18:26 | answer | added | T. Amdeberhan | timeline score: 6 | |
| Mar 11, 2022 at 6:21 | comment | added | Iosif Pinelis | I think your conjecture is true and have a very vague idea of how it could be proved, but at this point am far from an actual proof. | |
| Mar 11, 2022 at 4:40 | comment | added | JetfiRex | @IosifPinelis I wonder whether your examples can be a counterexample... or not? Since I am not sure how to prove a polynomial to be a counterexample... I have thought the examples of $Ax^2+Bx+C$ where $B\sim 0$, but failed to do so... | |
| Mar 11, 2022 at 4:25 | comment | added | Iosif Pinelis | Even a greater violation of the monotonicity of the single-peakedness in $r$: For $r\in\{1,\dots,40\}$, the polynomial $(10+x+x^2+10x^3)^r$ is single-peak only for $r\in\{30,32,34,36,37,38,39,40\}$. | |
| Mar 11, 2022 at 2:46 | comment | added | Iosif Pinelis | Not only can the product of two single-peak polynomials be non-single-peak, but also powers of a single-peak polynomial can be non-single-peak. E.g., the polynomial $(1 + x + 10 x^2)^r$ is non-single-peak for $r=2,\dots,9$. | |
| Mar 10, 2022 at 23:50 | history | asked | JetfiRex | CC BY-SA 4.0 |