Manuscript Oai211-A@1 · Oai211-A.tex · section · 3f3e4f63

Offspring-bounded labels without a third moment

Uniform path sums › Offspring-bounded labels without a third moment · lines 493–504

Oai211-A@1#eq:twowalks

For each strict ancestor-child pair $(k, i)$ , preorder exploration gives the exact identities

W (v) = path (v) \sum (k - i), W^{rev} (v) = path (v) \sum (i - 1) .

Indeed, the pending siblings to the right contribute $k - i$ ; the reversed order exchanges right and left siblings.

Displayed formulas in this passage

Oai211-A@1#eq:twowalks · line 497
$W (v) = path (v) \sum (k - i), W^{rev} (v) = path (v) \sum (i - 1) .$