OrderedTree from DyckPath

A Dyck path as the ordered tree whose depth-first contour it is: an up step opens a child, a down step closes it.

DyckPath → OrderedTreeinverse

FindStat's Mp00026. The inverse of DyckPath(OrderedTree).

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

Live

Explore

Each element of DyckPath at a size, and its image, applied in your browser; sizes past 7 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on OrderedTree. Its distribution over the images of DyckPath at each size is computed, and compared with the 171 statistics on DyckPath: 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 Mp00026

to ordered tree

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.

Sends a Dyck path to the ordered tree encoding the heights of the path.

Object	Image
[1,0]	[[]]
[1,0,1,0]	[[],[]]
[1,1,0,0]	[[[]]]
[1,0,1,0,1,0]	[[],[],[]]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00026 has the rest.