Timeline for Skew Kostka coefficients from Littlewood-Richardson Coefficients
Current License: CC BY-SA 3.0
7 events
when toggle format | what | by | license | comment | |
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Jun 30, 2013 at 20:03 | vote | accept | Per Alexandersson | ||
Jun 6, 2013 at 13:22 | comment | added | Per Alexandersson | Never mind, I think I managed to get the statement that I need, thank you for your effort! | |
Jun 6, 2013 at 10:42 | comment | added | Per Alexandersson | @Richard Stanley Ah, that explains it, but then I must be clearer with stating what I seek; The number of tableaux of shape $\lambda-\mu$ with weight $\nu$, (which I denote $K_{\lambda-\mu,\nu}$) is not the same as the number of skew tableaux of shape $\lambda/\mu$ and weight $\nu,$ which I denote $K_{\lambda/\mu,\nu}.$ (The latter has three free "parameter" partitions, while the first has essentially two.) What I would like is to be able to translate between $K_{\lambda/\mu,\nu}$ and $c_{\tau/\simga,\rho}.$ | |
Jun 5, 2013 at 19:40 | comment | added | Richard Stanley | $K_{\lambda-\mu,\nu}$ is simply another notation for $K_{\lambda/\mu,\nu}$. In general $\langle f,h_\mu\rangle$ is the coefficient of $m_\mu$ when $f$ is expanded in the basis of monomial symmetric functions. | |
Jun 5, 2013 at 18:59 | comment | added | Per Alexandersson | I don't really follow the first identity; Macdonald (5.14) says that $K_{\lambda−\mu,\nu}=\langle s_{\lambda/\mu},h_\nu\rangle$ but this is surely different from $K_{\lambda/\mu,\nu}$ which counts the number of skew tableaux of shape $\lambda/\mu$ and weight $\nu$? | |
Dec 13, 2012 at 6:51 | comment | added | Per Alexandersson | Thanky you, that answers my first question! | |
Dec 13, 2012 at 2:06 | history | answered | Richard Stanley | CC BY-SA 3.0 |