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Identifier

Mp00246: Ordered trees —rotate⟶ Ordered trees

Images

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Description

The rotation of an ordered tree.
Let $T$ be a rooted ordered tree with root $r$ and left most leaf $\ell$. It's rotation is obtained by attaching a leaf to $r$, removing the leaf $\ell$ and letting the vertex attached to $\ell$ be the new root.
By duality, this operation corresponds to rotation of polygon dissections.

Properties

bijective, graded

Sage code

def mapping(t):
    t = OrderedTree([t])
    branch_decomposition = []
    s = t[0]
    while s:
        branch_decomposition.append(s[1:])
        s = s[0]

    r = OrderedTree()
    for s in branch_decomposition:
        r = OrderedTree(s + [r])
    return OrderedTree(r)

Weight

Created

Feb 16, 2022 at 17:41 by Martin Rubey

Updated

Feb 16, 2022 at 21:03 by Martin Rubey