Hey guys, I'm finally enroled in a mathematics bachelor. My classes are going to start 31 this month. I want to thank for all your support. You've given me motivation and courage and inspiration (and also helped me a lot answering my stupid questions!). Without you nothing of this would be possible. Thanks.
Can anyone familiar with Littlewood-Richardson coefficients tell me is this "duality" is well-known: Given partitions $\lambda = (\lambda_1,\lambda_2,\dots,\lambda_n)$, $\mu$ and $\nu$ and such that $\lambda_i - \lambda_{i+1}\geq \mu_1$ for all $1\leq i\leq n-1$ and such that $\nu = \lambda + \sigma$ for some partition $\sigma$, the Littlewood-Richardson coefficient $c_{\lambda,\mu}^{\nu}$ is equal to the number of semistandard young tableaux of shape $\mu$ and type $\sigma$
Quick question: a hypersurface (eg vanishing set of some homogeneous polynomial) need not be connected in $P^1$, right? I can consider the vanishing locus of $X^2-Y^2$, which is [1:1] and [1:-1
], yes? I feel crazy and would like confirmation/denial
Hmm, good point. The homework I'm doing doesn't say hypersurface, it only says "Let $Y$ be a closed subscheme of $X=\PP^n_k$ defined by one homogenous equation $f$ of degree $d$."
@KarlKronenfeld Owners have some powers in a chat room, but mods have (more of) them across the chat network anyway, so it feels like pointless to me. But in the end, I don't care that much lol
@N3buchadnezzar . Ahh doesn't matter. I was going to say that it must lie on the real axis therefore your answer can't be purely imaginary. But I am wrong.
@Sawarnik if I put my solution and you give me the bounty .. it will be doing injustice to Jack .. there's very little difference and he answered it before me :D .. you can ask him to add all the steps and details .. then decide if you want to give him the bounty :)
@robjohn Argument for why the integral over $\int_\Gamma P(x)/(Q(x))$ goes to zero along the half circle from $R$ to $-R$ where $\deg P + 2 \leq \deg Q$ ?
