FromPermutation from Permutation
The increasing binary tree built by minimum-splitting recursion: the position of the smallest value roots the tree, everything before it recurses to the left, everything after it to the right.
Paired with ToPermutation, whose overload set (IncreasingBinaryTree among others) names this map's codomain. The root is always 1: every permutation of [n] holds the value 1, and heap order puts the global minimum at the top regardless of which permutation it came from. Built by real recursion, the same [label, left, right] nesting IncreasingBinaryTrees' cartesianTree builds.
Called as CombinatorialMap(x, "FromPermutation"). The head's page has its examples.
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Explore
Each element of Permutation at a size, and its image, applied in your browser; sizes past 7 are not offered.
Properties
Transport a statistic
Pick a statistic on IncreasingBinaryTree. Its distribution over the images of Permutation at each size is computed, and compared with the 323 statistics on Permutation: those that share it are the ones the map sends it to, as far as the sizes computed show.
No statistic is declared on IncreasingBinaryTree.