RightBranchBinaryTree from OrderedTree

An ordered tree as a binary tree with one fewer node: a vertex's right brother becomes its right child, its first child its left child, and the root goes.

OrderedTree → BinaryTreeinverse

FindStat's Mp00050, Sage's to_binary_tree_right_branch, the inverse of RightBranchOrderedTree. BinaryTree(OrderedTree) is the left-branch bijection, which is the constructor.

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

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Each element of OrderedTree 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 OrderedTree at each size is computed, and compared with the 21 statistics on OrderedTree: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic HeightLeftSubtreeSizeLeftSpineLeavesUnaryNodesBinaryNodesStrahlerNumberPathLengthExternalPathLengthPitchforksTreeFactorialLinearExtensionCountCollessIndexMaximalLeftBranchesDistinctSubtreesProtectionNumberRightChildCountRightSubtreeSizeSumParenthesisCodeValueBoundaryNodesNonBoundaryNodesNonRootBinaryNodesHookNumberVertexHeightSumRightRightPathCountRightRightRightPathCountRightRightRightRightPathCountRightRightLeftPathCountRightRightRightLeftPathCountRightLeftLeftPathCountRightLeftLeftLeftPathCountRightRightLeftLeftPathCountRightRightLeftRightPathCountRightForkRightLeftPatternCountForkRightRightLeftPatternCountSwapEquivalentTreeCountSwapEquivalentTreeCountLog Sizes 1 to

FindStat Mp00050

to binary tree: right brother = right child

Matched by value: our map agrees with FindStat's image on each of the 197 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

BijectionGraded mapas FindStat records them, checked by FindStat's contributors.

Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:

Object	Image
[]	.
[[]]	[.,.]
[[[]]]	[[.,.],.]
[[],[]]	[.,[.,.]]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00050 has the rest.