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BinaryTree from BinaryTreeParentArray ​

The binary tree an in-order parent array describes: a node below its parent goes left, above it right.

BinaryTreeParentArray → BinaryTreeinverse

Declines an array that isn't one: two roots, two left children, a cycle, or labels out of order.

Called as CombinatorialMap(x, "BinaryTree"). The head's page has its examples.

Also from

The same name out of other carriers, each its own implementation: DyckPath.