TAILIEUCHUNG - Lecture Analytic combinatorics (Part 2) - Chapter 4: Complex analysis, rational and meromorphic asymptotics

The purpose of this chapter is largely to serve as an accessible introduction or a refresher of basic notions regarding analytic functions. We start by recalling the elementary theory of functions and their singularities in a style tuned to the needs of analytic combinatorics. Cauchy’s integral formula expresses coefficients of analytic functions as contour integrals. Suitable uses of Cauchy’s integral formula then make it possible to estimate such coefficients by suitably selecting an appropriate contour of integration. | ANALYTIC COMBINATORICS PART TWO http 4. Complex Analysis Rational and Meromorphic Asymptotics ANALYTIC COMBINATORICS PART TWO Analytic Combinatorics Philippe Flajolet and Robert Sedgewick CAMBRIDGE http 4. Complex Analysis Rational and Meromorphic functions Roadmap Complex functions Rational functions Analytic functions and complex integration Meromorphic functions 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

• Kỹ thuật lập trình
• Analytic combinatorics
• Lecture Analytic combinatorics
• Combinatorial structures
• Complex analysis
• Meromorphic asymptotics
• Complex functions
• Unlabelled classes
• Labelled classes
• Symbolic method for parameters
• Compare algorithms
• Analysis of algorithms
• Scientific approach
• Computing values
• Types of recurrences
• Master theorem
• Ordinary generating functions
• Exponential generating functions
• Generating functions
• Asymptotic approximation
• Asymptotic expansions
• Manipulating asymptotic expansions
• Binary trees
• Combinatorial equivalences
• Properties of trees
• Algorithms on permutations
• Representations of permutations
• Situ permutation
• String searching
• Combinatorial properties of bitstrings
• Trie algorithms
• Hashing with separate chaining
• Birthday paradox
• Integer factorization
• Symbolic method
• Combinatorial class
• Labelled structures
• Labelled trees
• Combinatorial parameters
• Moment calculations
• Supercritical sequence schema
• Singularity analysis
• Standard function scale
• Transfer theorems
• Applications of singularity analysis
• Simple varieties of trees
• Saddle point asymptotics
• Modulus surfaces
• Saddle point bounds
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