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  "body": "\n## Statement\n\nThere is a generalization of this formula for skew shapes, \n\n$$s_{\\lambda/\\mu}(1,t,t^2,\\cdots) = \\sum_{S \\in E(\\lambda/\\mu)} \\prod_{(i,j) \\in \\lambda\\setminus S} \\frac{t^{\\lambda_j'-i}}{1-t^{h(i,j)}}$$\n\nwhere the sum is taken over *excited diagrams* of shape $\\lambda$ and boxes distributed according to $\\mu$.\n\nA variation on the same theme is given by Okounkov and Olshanski of the form\n\n$$\\frac{\\dim\\lambda/\\mu}{\\dim\\lambda}=\\frac{s^*_\\mu(\\lambda)}{|\\lambda|!/|\\mu|!},$$\n\nwhere $s^*_\\mu$ is the so-called shifted Schur function $s^*_\\mu(x_1,\\dots,x_n)=\\frac{\\det[(x_i+n-1)!/(\\mu_j+n-j)!]}{\\det[(x_i+n-i)!/(n-j)!]}$.\n",
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        "locator": "Hook length formula, section Semi-standard tableaux hook length formula \u003e Skew shape formula",
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