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  "body": "\n## Summary\n\nA graded poset is a [[partially ordered set|0QV2JS9RJ3]] with a rank function that goes up by exactly one along each covering step.\nThe elements then fall into levels, like the floors of a building.\nMany posets of combinatorics are graded: subsets by size, divisors by the number of prime factors, partitions by their size.\n\n## Explanations\n\n### L1 human\n\nPicture the Hasse diagram of a poset drawn so that every edge goes up exactly one level.\nIf this is possible, the poset is graded and the level of an element is its rank.\nThe subsets of $\\set{1, 2, 3}$ are graded by their number of elements: $\\varnothing$ has rank $0$ and $\\set{1, 2, 3}$ has rank $3$.\nA pentagon, where one side from bottom to top has two steps and the other has three, cannot be drawn this way.\n",
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