tailieunhanh - Lecture Analytic combinatorics (Part 2) - Chapter 5: Applications of rational and meromorphic asymptotics
The primary goal of this chapter is to provide combinatorial illustrations of the power of complex analytic methods, and specifically of the rational–meromorphic framework developed in the previous chapter. At the same time, we shift gears and envisage counting problems at a new level of generality. | ANALYTIC COMBINATORICS PART TWO http 5. Applications of Rational and Meromorphic Asymptotics 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 Bottom line from last lecture Analytic transfer for meromorphic GFs f z g z c 3N Compute the dominant pole a smallest real with g z 0 . Compute the residue h-1 -f ò g ò . Constant c is h-1 a. Exponential growth factor p is 1 a Not order 1 if g a 0. Adjust to slightly more complicated order M case. This lecture Numerous applications
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