$k$-protected vertices in unlabeled rooted plane trees

Keith Copenhaver

$k$-protected vertices in unlabeled rooted plane trees

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1606.00083 v3 pith:KHO4I3IB submitted 2016-06-01 math.CO

Keith Copenhaver This is my paper · ORCID

classification math.CO

keywords verticesapproachesaveragefindplaneprotectedrankrooted

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

abstract

We find a simple, closed formula for the proportion of vertices which are $k$-protected in all unlabeled rooted plane trees on $n$ vertices. We also find that, as $n$ goes to infinity, the average rank of a random vertex in a tree of size $n$ approaches 0.727649, and the average rank of the root of a tree of size $n$ approaches 1.62297.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Nonleaf Patterns in Trees: Protected Nodes and Fine Numbers
cs.DM 2019-08 accept novelty 6.0 of 10

A new pattern-enumeration formula for ordered trees that includes nonleaf-only pattern components is proven and used to count protected and unprotected nodes, stumps, and related tree families.

Pith tools