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  "body": "\n## Summary\n\nA linear extension of a [[partial order|0QV2JS9RJ3]] is a [[total order|0FRXBVVR03]] on the same set that keeps every relation of the partial order.\nEvery partial order has one, and the order is recovered as the intersection of all of them.\nLinear extensions are the basis of order dimension, of sorting problems, and of many counting questions about finite posets.\n\n## Explanations\n\n### L1 human\n\nA partial order is a set of rules of the form \"this comes before that\".\nA linear extension is a way to put all the elements in a single row so that every rule holds.\nFor the tasks \"dress\" before \"leave\" and \"eat\" before \"leave\", both rows dress, eat, leave and eat, dress, leave are linear extensions.\nThe row leave, dress, eat is not, since it breaks a rule.\n",
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