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  "body": "\n## Definition\n\nA Young diagram is a finite set $D \\subseteq \\mathbb{N} \\times \\mathbb{N}$ with this property: if $(i, j) \\in D$, $i' \\le i$ and $j' \\le j$, then $(i', j') \\in D$.\nThe elements of $D$ are the cells, or boxes, of the diagram.\nA cell $(i, j)$ is drawn as a unit square in row $i$ and column $j$, with rows numbered from the top.\n\n## Remarks\n\nThe rows of a Young diagram have weakly decreasing lengths $\\lambda_1 \\ge \\lambda_2 \\ge \\dots$. Thus a Young diagram with $n$ cells is the same as a [[partition|0404R9P9J3]] of $n$.\nThis drawing convention is the English one. The French convention draws row $0$ at the bottom.\nTransposing a diagram, $(i, j) \\mapsto (j, i)$, gives the diagram of the conjugate partition.\n\n## Explanations\n\n### L1 human\n\nA Young diagram draws a partition as rows of boxes, left-aligned, with the longest row at the top.\nThe partition $4 + 2 + 1$ gives rows of $4$, $2$ and $1$ boxes.\n",
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