On The Limiting Distributions of the Total Height On Families of Trees

zbMath1416.05021arXiv1702.04745MaRDI QIDQ5384242

Andrew Lohr, Doron Zeilberger

Publication date: 21 June 2019

Full work available at URL: https://arxiv.org/abs/1702.04745

zbMATH Keywords

labeled rooted treesrooted ordered trees

Mathematics Subject Classification ID

Trees (05C05) Exact enumeration problems, generating functions (05A15) Structural characterization of families of graphs (05C75) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Uses Software

• Maple
• GEPNER
• AlgFunEq
• Cheyne
• stCore
• A435

Cites Work

• On the Wiener index of random trees
• Brownian excursion area, wright's constants in graph enumeration, and other Brownian areas
• The depth first processes of Galton-Watson trees converge to the same Brownian excursion
• Integrals involving Rudin-Shapiro polynomials and sketch of a proof of Saffari's conjecture
• The continuum random tree. III
• Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf
• Automatic counting of tilings of skinny plane regions
• The Surprising Mathematics of Longest Increasing Subsequences
• Limit theorems for random trees.
• On the total heights of random rooted trees
• The Wiener Index of simply generated random trees
• Patterns in Random Permutations Avoiding the Pattern 132
• The enumeration of rooted trees by total height
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