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Inequality for hook numbers in Young diagrams

Denote coordinates of boxes in the Young diagram as $(i,j)$ for $i=1,\dots,\ell$ and $j=1,\dots,\lambda_i$. Consider the bijections $\varphi\colon(i,j)\mapsto(i,\lambda_i+1-j)$ and $\psi\colon(i,j)\m …
Bruno Le Floch's user avatar