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  "body": "\n## Summary\n\nThe permanent of a square matrix is the sum, over all permutations, of the products of one entry from each row and each column.\nIt is the [[determinant|00KDZRW4C0]] formula without the signs.\nFor the $0/1$ biadjacency matrix of a [[bipartite graph|0ZVQKTRKVQ]], it counts the [[perfect matchings|0NHK9MFFW9]].\nUnlike the determinant, it is believed to be hard to compute: computing the permanent of a $0/1$ matrix is #P-complete.\n\n## Explanations\n\n### L1 human\n\nPut $n$ rooks on an $n \\times n$ board so that no two share a row or a column, and multiply the entries under the rooks.\nThe permanent is the sum of these products over all such placements.\nThe determinant uses the same products but adds some of them with a minus sign.\nFor $\\begin{pmatrix} a \u0026 b \\\\ c \u0026 d \\end{pmatrix}$ the permanent is $ad + bc$, while the determinant is $ad - bc$.\n",
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    "tag": "X9B1XETBPF"
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/X9B/X9B1XETBPF.md",
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  "tag": "X9B1XETBPF",
  "uri": "m2://X9B1XETBPF",
  "url": "https://math2.tamnd.com/wiki/permanent/",
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    "tag": "X9B1XETBPF",
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