Mirror from OrderedTree

The left-right symmetry of an ordered tree: every node's children in the opposite order.

OrderedTree → OrderedTreeinvolution

FindStat's Mp00048, an involution.

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

Live

Explore

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 OrderedTree. 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 RootDegreeHeightLeavesNonRootInternalNodesLargestOutDegreeStrahlerNumberPathLengthTreeFactorialLinearExtensionCountDistinctSubtreesProtectionNumberBoundaryLengthTrunkLengthBreadthLongestPathVertexCountAutomorphismGroupSizeInequivalentIncreasingTreeCountOneProtectedNodeCountTwoProtectedNodeCountPruningNumberBoundaryLengthBeyondTrunk Sizes 1 to

Also from

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

FindStat Mp00048

left-right symmetry

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 mapInvolutionas FindStat records them, checked by FindStat's contributors.

Return the left-right symmetrized tree of an ordered tree.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00048 has the rest.