Timeline for sum of the character of the symmetric group
Current License: CC BY-SA 2.5
15 events
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| Dec 18, 2013 at 16:11 | comment | added | Grigory M | Related: roots of permutations | |
| Feb 28, 2011 at 2:59 | comment | added | Hanxiong Zhang | Thanks for the link and reference, Darij. But I do not think that Theorem 2.1 actually simplifies anything, it replace the sum with something not explicit and still intractable... | |
| Feb 27, 2011 at 13:03 | comment | added | darij grinberg | Oh wait. This is not an answer to (0). Still it solves a similar sum (namely, $\sum_{\nu} \frac{\chi_{\nu}}{\chi_{\nu}\left(1\right)}$. | |
| Feb 27, 2011 at 12:54 | comment | added | darij grinberg | For (0), check Theorem 2.1 in math.ipm.ac.ir/pournaki/Main%20Files/1-Papers/Accepted-3/… . I am pretty sure it does NOT require $g\in G^{\prime}$. It yields a formula for the sum of all irreducible characters applied to some group element. It is zero if the group element is not a commutator. The thing should now boil down to proving that a permutation is a commutator if and only if its cycle partition has an even number of even parts. Am I right? | |
| Feb 27, 2011 at 12:47 | comment | added | darij grinberg | Actually I have requested a categorification of (1) on MO some time ago: mathoverflow.net/questions/45065/… . | |
| Feb 27, 2011 at 12:44 | comment | added | darij grinberg | (1) is answered in www-igm.univ-mlv.fr/~berstel/Lothaire/AlgCWContents.html "The Plactic Monoid" as well. | |
| Feb 27, 2011 at 9:22 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 8:42 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 7:46 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 7:11 | vote | accept | Hanxiong Zhang | ||
| Feb 27, 2011 at 6:54 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 6:50 | answer | added | Philippe Nadeau | timeline score: 10 | |
| Feb 27, 2011 at 6:32 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 6:21 | history | edited | Hanxiong Zhang | CC BY-SA 2.5 |
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| Feb 27, 2011 at 5:56 | history | asked | Hanxiong Zhang | CC BY-SA 2.5 |