Skip to main content
7 events
when toggle format what by license comment
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