Protected Branches in Ordered Trees

DOI10.4208/jms.v56n1.23.01OpenAlexW4310347657MaRDI QIDQ5882292

Sheng-Liang Yang, Lin Yang

Publication date: 15 March 2023

Published in: Journal of Mathematical Study (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/jms.v56n1.23.01

zbMATH Keywords

Catalan numbergenerating functionordered treeplanted treebushprotected branchunprotected branch

Mathematics Subject Classification ID

Trees (05C05) Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Asymptotic enumeration (05A16)

Uses Software

• OEIS

Cites Work

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• \(k\)-protected vertices in binary search trees
• The uplift principle for ordered trees
• Notes on protected nodes in digital search trees
• Protected points in \(k\)-ary trees
• Descent distribution on Catalan words avoiding a pattern of length at most three
• Old and young leaves on plane trees
• Lagrange inversion: when and how
• Enumerations of ordered trees
• Enumeration of plane trees by branches and endpoints
• A short proof of an identity of Touchard's concerning Catalan numbers
• Two combinatorial statistics on Dyck paths
• Ordered trees with prescribed root degrees, node degrees, and branch lengths
• A bijection between ordered trees and 2-Motzkin paths and its many consequences
• \(k\)-protected vertices in unlabeled rooted plane trees
• Protected points in ordered trees
• Protection number in plane trees

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