7.   Applications of Singularity Analysis



VII.1 A roadmap to singularity analysis asymptotics


VII.2 Sets and the exp–log schema


VII.3 Simple varieties of trees and inverse functions


VII.4 Tree-like structures and implicit functions


VII.5 Unlabelled non-plane trees and P´olya operators


VII.6 Irreducible context-free structures


VII.7 The general analysis of algebraic functions


VII.8 Combinatorial applications of algebraic functions


VII.9 Ordinary differential equations and systems


VII.10 Singularity analysis and probability distributions


VII.11 Perspective


Web Exercises

VII.1

Use the tree-like schema to develop an asymptotic expression for the number of bracketings with $N$ leaves (see Example I.15 on page 69 and Note VII.19 on page 474)



Selected Experiments

Program VII.1

Do r- and θ-plots of the GF for bracketings (see Web Exercise VII.1).