Timeline for Expressing power sum symmetric polynomials in terms of lower degree power sums
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2010 at 13:07 | vote | accept | Peter Erskin | ||
| Aug 28, 2010 at 1:32 | comment | added | Gjergji Zaimi | @Qiaochu: Yes, I don't know why I wrote it like that, same thing I guess. @Peter Erskin, I mentioned above that combinatorialists care about the case of infinitely many variables. What reasons do we have to believe that $a_{k,\rho}$ has any nice form? They aren't even integers, and they depend on $N$... | |
| Aug 27, 2010 at 15:54 | comment | added | Qiaochu Yuan | @Gjergji: instead of the first identity I would just say that the trace of the matrix you wrote down is p_{k-n} and leave it at that. | |
| Aug 27, 2010 at 15:40 | comment | added | Peter Erskin | Thank you very much for the explicit (in contrast to previous suggestions) formula and for the clarification! The formula really works and it looks simpler than the determinant-of-determinants that I proposed in the "Note Added". Unfortunately, I do not see how to present your expression for $ p_k$ in the form similar to your formula for $ e_n $. Is it possible to find the combinatorial coefficients $ a_{k;\rho} $ as discussed in my question? | |
| Aug 27, 2010 at 12:06 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
added 648 characters in body
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| Aug 27, 2010 at 11:16 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |