RightBranchOrderedTree from BinaryTree

A binary tree as an ordered tree with one more vertex: a right child becomes its parent's right brother, a left child its parent's first child.

BinaryTree → OrderedTreeinverse

FindStat's Mp00015, Sage's to_ordered_tree_right_branch, a bijection. Its inverse is RightBranchBinaryTree. OrderedTree(BinaryTree) is the left-branch bijection, which is the constructor.

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

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Each element of BinaryTree 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 OrderedTree. Its distribution over the images of BinaryTree at each size is computed, and compared with the 37 statistics on BinaryTree: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic RootDegreeHeightLeavesNonRootInternalNodesLargestOutDegreeStrahlerNumberPathLengthTreeFactorialLinearExtensionCountDistinctSubtreesProtectionNumberBoundaryLengthTrunkLengthBreadthLongestPathVertexCountAutomorphismGroupSizeInequivalentIncreasingTreeCountOneProtectedNodeCountTwoProtectedNodeCountPruningNumberBoundaryLengthBeyondTrunk Sizes 1 to

FindStat Mp00015

to ordered tree: right child = right brother

Matched by value: our map agrees with FindStat's image on each of the 196 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 an ordered tree of size $n+1$ by the following recursive rule:

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00015 has the rest.