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.

Live

Explore

Each element of BinaryTreeParentArray at a size, and its image, applied in your browser; sizes past 6 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on BinaryTree. Its distribution over the images of BinaryTreeParentArray at each size is computed, and compared with the 0 statistics on BinaryTreeParentArray: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic HeightLeftSubtreeSizeLeftSpineLeavesUnaryNodesBinaryNodesStrahlerNumberPathLengthExternalPathLengthPitchforksTreeFactorialLinearExtensionCountCollessIndexMaximalLeftBranchesDistinctSubtreesProtectionNumberRightChildCountRightSubtreeSizeSumParenthesisCodeValueBoundaryNodesNonBoundaryNodesNonRootBinaryNodesHookNumberVertexHeightSumRightRightPathCountRightRightRightPathCountRightRightRightRightPathCountRightRightLeftPathCountRightRightRightLeftPathCountRightLeftLeftPathCountRightLeftLeftLeftPathCountRightRightLeftLeftPathCountRightRightLeftRightPathCountRightForkRightLeftPatternCountForkRightRightLeftPatternCountSwapEquivalentTreeCountSwapEquivalentTreeCountLog Sizes 1 to

Also from

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