LeftBorderSymmetry from BinaryTree

Reverse the order of the right subtrees hanging off the left border, applying the same symmetry inside each.

BinaryTree → BinaryTreeinvolution

FindStat's Mp00018, an involution.

Called as CombinatorialMap(x, "LeftBorderSymmetry"). 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 BinaryTree. 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 HeightLeftSubtreeSizeLeftSpineLeavesUnaryNodesBinaryNodesStrahlerNumberPathLengthExternalPathLengthPitchforksTreeFactorialLinearExtensionCountCollessIndexMaximalLeftBranchesDistinctSubtreesProtectionNumberRightChildCountRightSubtreeSizeSumParenthesisCodeValueBoundaryNodesNonBoundaryNodesNonRootBinaryNodesHookNumberVertexHeightSumRightRightPathCountRightRightRightPathCountRightRightRightRightPathCountRightRightLeftPathCountRightRightRightLeftPathCountRightLeftLeftPathCountRightLeftLeftLeftPathCountRightRightLeftLeftPathCountRightRightLeftRightPathCountRightForkRightLeftPatternCountForkRightRightLeftPatternCountSwapEquivalentTreeCountSwapEquivalentTreeCountLog Sizes 1 to

FindStat Mp00018

left border symmetry

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

Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00018 has the rest.