Timeline for Negative coefficient in an almost cyclotomic polynomial
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 7, 2015 at 10:07 | vote | accept | Flo140 | ||
| Sep 7, 2015 at 9:35 | vote | accept | Flo140 | ||
| Sep 7, 2015 at 9:35 | |||||
| Sep 4, 2015 at 15:32 | answer | added | Peter Mueller | timeline score: 6 | |
| Sep 4, 2015 at 14:44 | comment | added | Flo140 | At first, i was studying some orthogonal function (in control theory) and more specifically its sign. The orthogonal function depends of four parameters and its linked with a polynomial (such as the one of the question). After a big number of numerical tests, i observe that when i take the parameters in the form $(abc,abd,acd,bcd)$ the polynomial always has a negative coefficient (that is important to understand the orthogonal function). I don't know if it's clear, it is always complicated to summarize a problem. | |
| Sep 4, 2015 at 13:50 | comment | added | Louis Deaett | Yes, I certainly agree with you. My observation above is well short of answering the question, sadly. I'd also like to see how this could be resolved. I'd also be interested in knowing how this question came up to begin with, if it's at all easy to explain. | |
| Sep 4, 2015 at 13:14 | comment | added | Flo140 | When we write $P(X)=\prod \phi_{m}(X)$ it's not obvious for me that we can deduce the sign of the coefficient of $P$. For exemple if we consider $$Q(X)=\frac{(1-X^{ab})(1-X^{ac})(1-X^{bc})}{(1-X^{a})(1-X^{b})(1-X^{c})}$$ we have also $Q(X)=\prod \phi_{m}(X)$ but in this case it's clear that $Q$ only has non negative coefficient. | |
| Sep 4, 2015 at 12:42 | comment | added | Flo140 | @Louis the references you give seem really interesting... | |
| Sep 3, 2015 at 22:46 | comment | added | Louis Deaett | Note that $P(x)=\prod \Phi_m(x)$, where the product is over all $1<m<abcd$ dividing $abcd$. | |
| Sep 3, 2015 at 22:17 | comment | added | Louis Deaett | Related question I asked at mathoverflow.net/questions/214784/… | |
| Sep 3, 2015 at 12:12 | history | edited | Richard Stanley | CC BY-SA 3.0 |
fixed typo
|
| Sep 3, 2015 at 10:04 | review | First posts | |||
| Sep 3, 2015 at 10:19 | |||||
| Sep 3, 2015 at 9:56 | history | asked | Flo140 | CC BY-SA 3.0 |