Timeline for Computing a determinant involving roots of unity
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 24, 2017 at 14:16 | comment | added | Neil Strickland | @ViditNanda The absolute value was conjectured by SylvainJULIEN, and easily verified numerically. It is also easily visible numerically that $\Delta(d)=d^{d/2}i_{m_d}$ for some $m_d$ which only matters mod $4$ and which you can tabulate. You then observe that $m_{d+8}=m_{7-d}=m_d\pmod{4}$, and from there you only need a little guesswork. | |
| Jun 23, 2017 at 23:00 | comment | added | GH from MO | I confirmed your formula below. | |
| Jun 23, 2017 at 22:51 | comment | added | Vidit Nanda | Amazing. Did you use the OEIS, or are the origins of this formula voodoo-theoretic? | |
| Jun 23, 2017 at 19:20 | history | edited | Neil Strickland | CC BY-SA 3.0 |
Replaced table of values of m_d by a formula
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| Jun 23, 2017 at 19:08 | comment | added | Gerhard Paseman | The matrix determinant is equivalent, as Federico mentioned above, to a scalar t times the determinant of a modified Vandermonde with first column all 1's and remaining columns the ijth power of the root of unity. If you can come up with a proof or expression for t(d), you might get a proof of the general result. Gerhard "T For Two Or Three" Paseman, 2017.06.23. | |
| Jun 23, 2017 at 18:10 | history | answered | Neil Strickland | CC BY-SA 3.0 |