Rotation from OrderedTree

Attach a leaf to the root, remove the leftmost leaf, and let the vertex it hung from become the root.

OrderedTree → OrderedTreebijection

FindStat's Mp00246, a bijection corresponding to rotating a polygon dissection.

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

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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

FindStat Mp00246

rotate

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.

The rotation of an ordered tree.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00246 has the rest.