tailieunhanh - Lecture Analytic combinatorics (Part 2) - Chapter 7: Applications of singularity analysis
Singularity analysis paves the way to the analysis of a large quantity of generating functions, as provided by the symbolic method expounded in Chapters I–III. In this chapter we illustrate this situation with numerous examples related to languages, permutations, trees, and graphs of various sorts. As in chapter 5, most analyses are organized into broad classes called schemas. | ANALYTIC COMBINATORICS PART TWO http 7. Applications of Singularity Analysis Analytic combinatorics overview A. SYMBOLIC METHOD 1. OGFs 2. EGFs 3. MGFs B. COMPLEX ASYMPTOTICS 4. Rational Meromorphic 5. Applications of R M 6. Singularity Analysis 7. Applications of SA 8. Saddle point specification SYMBOLIC METHOD GF equation COMPLEX ASYMPTOTICS asymptotic estimate T desired result 2 ANALYTIC COMBINATORICS CAMBRIDGE Analytic Combinatorics Philippe Flajolet and Robert Sedgewick PART TWO 7. Applications of Singularity Analysis Simple varieties of trees Labelled sets Mappings Tree-like classes http .
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