tailieunhanh - Lecture Analytic combinatorics (Part 2) - Chapter 6: Singularity analysis

In this chapter, we present a general approach to the analysis of coefficients of generating functions that is not restricted to polar singularities and extends to a large class of functions that have moderate growth or decay at their dominant singularities. This chapter presents the following content: Prelude, standard function scale, singularity analysis, schemas and transfer theorems. | ANALYTIC COMBINATORICS PART TWO http 6. 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 Warning entering deep water symbolic method rational asymptotics meromorphic asymptotics singularity analysis Good news End results are often broadly applicable and not complicated. Bad news Technical skill is often required to prove them to be valid This lecture Overview of approach. Statements of several transfer theorems. For full details refer always to The Book.

• Kỹ thuật lập trình
• Analytic combinatorics
• Lecture Analytic combinatorics
• Combinatorial structures
• Singularity analysis
• Standard function scale
• Transfer theorems