Combinatorial differential operators in: Faà di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted trees

Trees (05C05) Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Paths and cycles (05C38) Distance in graphs (05C12)

Cites Work

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Hypergraphs and a functional equation of Bouwkamp and de Bruijn
On the distribution of depths in increasing trees
On the asymptotic internal path length and the asymptotic Wiener index of random Split trees
Context-free grammars, differential operators and formal power series
Colored species, \(c\)-monoids, and plethysm. I
The spectral Carathéodory-Fejér problem
Chain rules for higher derivatives
Éclosions combinatoires appliquées à l'inversion multidimensionnelle des séries formelles. (Combinatorial bloomings applied to the multidimensional inversion of formal series)
Branching processes in the analysis of the heights of trees
Une nouvelle demonstration combinatoire des formules d'inversion de Lagrange
Une théorie combinatoire des séries formelles
Cayley's formula for multidimensional trees
William Chen grammars and derivations in trees and arborescences
Generalization of the formula of Faa di Bruno for a composite function with a vector argument
A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
Two element lattice permutation numbers and their \(q\)-generalization
Sur les cycles des substitutions.
Emergence of Scaling in Random Networks
Limiting Distributions for Path Lengths in Recursive Trees
A note on the height of binary search trees
A Probability Model of a Pyramid Scheme
On the Altitude of Nodes in Random Trees
On the internal path length ofd-dimensional quad trees
Note on the heights of random recursive trees and random m‐ary search trees
The Curious History of Faa di Bruno's Formula
On the Variance of the Height of Random Binary Search Trees
A Multivariate Faa di Bruno Formula with Applications
An Algebraic Theory of Integration Methods
Prehistory of FaÃ Â di Bruno's Formula
Derivatives of composite functions

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