Timeline for Sum of irreducible complex character degrees for alternating groups
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jul 27, 2015 at 8:59 | vote | accept | Sven Wirsing | ||
| Jun 12, 2015 at 17:35 | comment | added | Richard Stanley | Following up on my previous comment, an interesting related result is that $\sum_\lambda f^\lambda (-1)^{\frac 12(n-\mathrm{rank}(\lambda))}$ equals the coefficient of $x^n/n!$ in $e^{x-\frac{x^2}{2}}$. Here $\lambda$ ranges over all self-conjugate partitions of $n$, $f^\lambda$ is the dimension of the corresponding symmetric group character, and $\mathrm{rank}(\lambda)$ is size of the Durfee square of $\lambda$ (the largest $i$ for which $\lambda_i\geq i$). | |
| Jun 10, 2015 at 13:05 | comment | added | Sven Wirsing | Thank you, maybe its nice to know difference to the corresponding sum for $S_n$. Is this also in this tool? | |
| Jun 8, 2015 at 17:00 | answer | added | Stefan Kohl♦ | timeline score: 3 | |
| Jun 8, 2015 at 16:37 | comment | added | Richard Stanley | This is equivalent to finding the sum of the degrees of all self-conjugate characters of the symmetric group $S_n$. It appears in oeis.org/A067136, but I don't think that any reasonable formula is known. | |
| Jun 8, 2015 at 13:14 | history | asked | Sven Wirsing | CC BY-SA 3.0 |